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Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function
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作者 Junrui Yue Yun Zhang Qingyue Bai 《Open Journal of Applied Sciences》 2024年第1期63-69,共7页
This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones a... This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique. 展开更多
关键词 Fourth-Order Three-Point Boundary Value Problem Sign-Changing Green’s Function Fixed Point Index Iterative Technique Monotone positive solution EXISTENCE
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Semi-analytical solution for mechanical analysis of tunnels crossing strike-slip fault zone considering nonuniform fault displacement and uncertain fault plane position
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作者 YANG Heng-hong WANG Ming-nian +1 位作者 YU Li ZHANG Xiao 《Journal of Central South University》 SCIE EI CAS CSCD 2024年第6期2116-2136,共21页
The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-e... The tunnel subjected to strike-slip fault dislocation exhibits severe and catastrophic damage.The existing analysis models frequently assume uniform fault displacement and fixed fault plane position.In contrast,post-earthquake observations indicate that the displacement near the fault zone is typically nonuniform,and the fault plane position is uncertain.In this study,we first established a series of improved governing equations to analyze the mechanical response of tunnels under strike-slip fault dislocation.The proposed methodology incorporated key factors such as nonuniform fault displacement and uncertain fault plane position into the governing equations,thereby significantly enhancing the applicability range and accuracy of the model.In contrast to previous analytical models,the maximum computational error has decreased from 57.1%to 1.1%.Subsequently,we conducted a rigorous validation of the proposed methodology by undertaking a comparative analysis with a 3D finite element numerical model,and the results from both approaches exhibited a high degree of qualitative and quantitative agreement with a maximum error of 9.9%.Finally,the proposed methodology was utilized to perform a parametric analysis to explore the effects of various parameters,such as fault displacement,fault zone width,fault zone strength,the ratio of maximum fault displacement of the hanging wall to the footwall,and fault plane position,on the response of tunnels subjected to strike-slip fault dislocation.The findings indicate a progressive increase in the peak internal forces of the tunnel with the rise in fault displacement and fault zone strength.Conversely,an augmentation in fault zone width is found to contribute to a decrease in the peak internal forces.For example,for a fault zone width of 10 m,the peak values of bending moment,shear force,and axial force are approximately 46.9%,102.4%,and 28.7% higher,respectively,compared to those observed for a fault zone width of 50 m.Furthermore,the position of the peak internal forces is influenced by variations in the ratio of maximum fault displacement of the hanging wall to footwall and the fault plane location,while the peak values of shear force and axial force always align with the fault plane.The maximum peak internal forces are observed when the footwall exclusively bears the entirety of the fault displacement,corresponding to a ratio of 0:1.The peak values of bending moment,shear force,and axial force for the ratio of 0:1 amount to approximately 123.8%,148.6%,and 111.1% of those for the ratio of 0.5:0.5,respectively. 展开更多
关键词 strike-slip fault tunnel engineering semi-analytical solution fault zone width nonuniform fault displacement uncertain fault plane position
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Positive Pseudo-Symmetric Solutions for Some Nonlinear Systems at Resonance
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作者 张莉 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2010年第4期495-498,共4页
By means of an extension of Mawhin's continuation theorem due to Ge,this work shows the existence of at least one positive pseudo-symmetric solution of the multi-point boundary value system.The interesting fact is th... By means of an extension of Mawhin's continuation theorem due to Ge,this work shows the existence of at least one positive pseudo-symmetric solution of the multi-point boundary value system.The interesting fact is that the nonlinear terms are involved in the first order derivatives. 展开更多
关键词 positive pseudo-symmetric solutions boundary value system RESONANCE
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POSITIVE SOLUTIONS WITH HIGH ENERGY FOR FRACTIONAL SCHRODINGER EQUATIONS
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作者 郭青 赵雷嘎 《Acta Mathematica Scientia》 SCIE CSCD 2023年第3期1116-1130,共15页
In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical expo... In this paper, we study the Schrodinger equations (-△)^(s)u + V(x)u = a(x)|u|^(p-2)u + b(x)|u|^(q-2)u, x∈R^(N),where 0 < s < 1, 2 < q < p < 2_(s)^(*), 2_(s)^(*) is the fractional Sobolev critical exponent. Under suitable assumptions on V, a and b for which there may be no ground state solution, the existence of positive solutions are obtained via variational methods. 展开更多
关键词 fractional Schr?dinger equations positive solution concentration compactness principle
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Hermite Positive Definite Solution of the Quaternion Matrix Equation Xm + B*XB = C
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作者 Yiwen Yao Guangmei Liu +1 位作者 Yanting Zhang Jingpin Huang 《Journal of Applied Mathematics and Physics》 2023年第11期3760-3772,共13页
This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation X<sup>m</sup>+ B*XB = C (m > 0) and its iterative ... This paper discusses the necessary and sufficient conditions for the existence of Hermite positive definite solutions of the quaternion matrix equation X<sup>m</sup>+ B*XB = C (m > 0) and its iterative solution method. According to the characteristics of the coefficient matrix, a corresponding algebraic equation system is ingeniously constructed, and by discussing the equation system’s solvability, the matrix equation’s existence interval is obtained. Based on the characteristics of the coefficient matrix, some necessary and sufficient conditions for the existence of Hermitian positive definite solutions of the matrix equation are derived. Then, the upper and lower bounds of the positive actual solutions are estimated by using matrix inequalities. Four iteration formats are constructed according to the given conditions and existence intervals, and their convergence is proven. The selection method for the initial matrix is also provided. Finally, using the complexification operator of quaternion matrices, an equivalent iteration on the complex field is established to solve the equation in the Matlab environment. Two numerical examples are used to test the effectiveness and feasibility of the given method. . 展开更多
关键词 QUATERNION Matrix Equation Hermite positive Definite solution Matrix Inequality ITERATIVE CONVERGENCE
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SYMMETRIC POSITIVE DEFINITE SOLUTIONS OF MATRIX EQUATIONS (AX,XB)=(C,D) AND AXB=C 被引量:1
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作者 戴华 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 1996年第2期56+52-55,共5页
The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive de... The symmetric positive definite solutions of matrix equations (AX,XB)=(C,D) and AXB=C are considered in this paper. Necessary and sufficient conditions for the matrix equations to have symmetric positive definite solutions are derived using the singular value and the generalized singular value decompositions. The expressions for the general symmetric positive definite solutions are given when certain conditions hold. 展开更多
关键词 numerical algebra MATRIX EQUATION symmetric positive definite solution
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On the Problem of All Equal Positive Odd Number Solutions of the Dissemination of the Ends' Guess 被引量:1
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作者 刘元宗 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第2期108-109,共2页
The thesis is concerned with the problem of the dissemination of the Ends’ guess and offers the formula of all equal positive odd number solutions.
关键词 Ends’ guess DISSEMINATION all equal positive odd number solutions
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The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms
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作者 WANG Ji-nan SUN Da-wei 《Chinese Quarterly Journal of Mathematics》 2024年第3期315-323,共9页
We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global min... We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough. 展开更多
关键词 Kirchhoff-type equation The existence positive solution Variational method
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Positive Solutions of a Semilinear Elliptic Equation with Coefficient That Changes Sign
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作者 马如云 姚庆六 李宝麟 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第4期10-14,共5页
We prove the existence of a positive solution to the problem-Δu=a(x)f(u), x∈Ω, u(x)=0,x∈Ω,where Ω is a bounded domain in R n with smooth boundary, a(x) is allowed to change sign.
关键词 elliptic equation positive solution Leray-Schauder fixed point theorem
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Existence of Multiple Positive Solutions for Higher-Order p-Laplacian Boundary Value Problems
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作者 贺小明 葛渭高 《Journal of Beijing Institute of Technology》 EI CAS 2002年第2期212-216,共5页
The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which e... The existence of multiple positive solutions for a class of higher order p Laplacian boundary value problem is studied. By means of the Leggett Williams fixed point theorem in cones, existence criteria which ensure the existence of at least three positive solutions of the boundary value problem are established. 展开更多
关键词 positive solutions cone Leggett Williams fixed point theorem p Laplacian boundary value problems
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Existence of Positive Solutions for Nonlinear Conjugate Boundary Value Problems
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作者 菅典兵 董正华 《Chinese Quarterly Journal of Mathematics》 CSCD 2002年第2期87-93,共7页
The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0... The present paper is concerned with the existence of positive solutions of the (k,n-k) conjugate boundary value problems(-1) n-k u (h) (t)=λa(t)f(u(t)),t∈(0,1), u (i) (0)=0,0≤i≤k-1, u (j) (0)=0,0≤j≤n-k-1,where λ is a positive parmeter. Krasnoselsii’s fixed point theorem is employed to obtain the existence criteria for positive solution. 展开更多
关键词 existence theorem positive solutions conjugate boundary value problem
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An Existence Theorem of Positive Solution for Fourth-order Superlinear Semipositone Eigenvalue Problems
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作者 江秀芬 姚庆六 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第2期64-68,共5页
In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam wh... In this paper we investigate the existence of positive solution for a class of fourth_order superlinear semipositone eigenvalue problems. This class of problems usually describes the deformation of the elastic beam whose both end_points are fixed. 展开更多
关键词 elastic beam equation existence of positive solution SEMIpositONE fixed point theorem on cone
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Asymptotic Behavior and Nonexistence of Positive Solutions of Delay Difference Equations *L
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作者 彭名书 徐千里 《Journal of Beijing Institute of Technology》 EI CAS 1999年第1期25-30,共6页
Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some i... Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included. 展开更多
关键词 OSCILLATION asymptotic behavior positive solution neutral delay difference equation NONLINEARITY
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Existence of Positive Solutions for a Class of Degenerate and Nondegenerate Stable Diffusion Models
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作者 张彦肖 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第3期50-56,共7页
This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive... This paper is concerned with a class of degenerate and nondegenerate stable diffusion models.By using the upper and lower solution method and Schauder fixed point principle,the author studies the existence of positive solutions for these stable_diffusion models under some conditions. 展开更多
关键词 weak upper and lower solutions elliptic system positive solution
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Existence of solutions and positive solutions to a fourth-order two-point BVP with second derivative 被引量:12
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作者 姚庆六 《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》 SCIE EI CAS CSCD 2004年第3期104-108,共5页
Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of ... Several existence theorems were established for a nonlinear fourth-order two-point boundary value problem with second derivative by using Leray-Schauder fixed point theorem, equivalent norm and technique on system of integral equations. The main conditions of our results are local. In other words, the existence of the solution can be determined by considering the height of the nonlinear term on a bounded set. This class of problems usually describes the equilibrium state of an elastic beam which is simply supported at both ends. 展开更多
关键词 Nonlinear fourth-order equation Two-point boundary value problem solution and positive solution EXISTENCE Fixed point theorem
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MULTIPLE POSITIVE SOLUTIONS OF SINGULAR THIRD-ORDER PERIODIC BOUNDARY VALUE PROBLEM 被引量:21
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作者 孙经先 刘衍胜 《Acta Mathematica Scientia》 SCIE CSCD 2005年第1期81-88,共8页
This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2... This paper deals with the singular nonlinear third-order periodic boundary value problem u'' + p(3)u = f (t, u), 0 less than or equal to t less than or equal to 2pi, with u((i)) (0) = u((i)) (2pi), i = 0, 1, 2, where p is an element of (Graphics) and f is singular at t = 0, t = 1 and u = 0. Under suitable weaker conditions than those of [1], it is proved by constructing a special cone in C[0, 2pi] and employing the fixed point index theory that the problem has at least one or at least two positive solutions. 展开更多
关键词 singular boundary value problem third-order differential system positive solution
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EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS WITH DEVIATING ARGUMENTS 被引量:23
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作者 LuShiping GeWeigao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2002年第4期382-390,共9页
By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(... By means of an abstract continuation theorem, the existence criteria are established for the positive periodic solutions of a neutral functional differential equation d N d t=N(t)[a(t)-β(t)N(t)-b(t)N(t-σ(t))-c(t)N′(t-τ(t))]. 展开更多
关键词 positive periodic solution abstract continuation theorem neutral functional differential equation.
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EXISTENCE AND UNIQUENESS OF POSITIVE SOLUTIONS TO A CLASS OF SEMILINEAR ELLIPTIC SYSTEMS 被引量:9
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作者 钟金标 陈祖墀 《Acta Mathematica Scientia》 SCIE CSCD 2002年第4期451-458,共8页
In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the a... In this paper an existence and uniqueness theorem of positive solutions to a class of semilinear elliptic systems is proved. Also, a necessary condition for the existence of the positive solution is obtained. As the application of the main theorem, two examples are given. 展开更多
关键词 positive solution semilinear elliptic system compact and positive operator
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AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS 被引量:12
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作者 Jiang Xiufen Yao Qingliuof Math., Northwest Normal Univ., Lanzhou 730070. 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2001年第3期237-240,共4页
By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam w... By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points. 展开更多
关键词 Elastic beam equation positive solution EXISTENCE fixed point theorem on cone.
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Positive Solutions Bifurcating from Zero Solution in a Lotka-Volterra Competitive System with Cross-Diffusion Effects 被引量:8
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作者 ZHANG Cun-hua YAN Xiang-ping 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第3期342-352,共11页
A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. B... A strongly coupled elliptic system under the homogeneous Dirichlet boundary condition denoting the steady-state system of the Lotka-Volterra two-species competitive system with cross-diffusion effects is considered. By using the implicit function theorem and the Lyapunov- Schmidt reduction method, the existence of the positive solutions bifurcating from the trivial solution is obtained. Furthermore, the stability of the bifurcating positive solutions is also investigated by analyzing the associated characteristic equation. 展开更多
关键词 Lotka-Volterra competitive system CROSS-DIFFUSION positive solution Steady state bifurcation Stability.
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