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Several Existence Theorems for Positive Radial Solutions to a Semilinear Elliptic BVP 被引量:3
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作者 姚庆六 《Northeastern Mathematical Journal》 CSCD 2001年第2期169-174,共6页
The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and se... The existence of positive radial solutions to the second order semilinear elliptic BVPΔu(X)+g(|X|)f(u(X))=0, R 1<|X|<R 2, u(X)=0, |X|=R 1 or |X|=R 2is considered. A general existence criterion and several existence theorems of positive radial solution are established. Here it is not required that lim l→0f(l)/l and lim l→∞f(l)/l exist. 展开更多
关键词 second order elliptic equation Dirichlet BVP in annulus positive radial solution existence theorem
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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 Solution for a Singular Third-order Two-point Boundary Value Problem 被引量:1
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作者 姚庆六 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第1期61-66,共6页
By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′(t)+f(t,u(t),u′(t))=0,0〈t〈1,u(0)=u′(0)=u′... By constructing suitable Banach space, an existence theorem is established under a condition of linear growth for the third-order boundary value problem u″′(t)+f(t,u(t),u′(t))=0,0〈t〈1,u(0)=u′(0)=u′(1)=0, where the nonlinear term contains first and second derivatives of unknown function. In this theorem the nonlinear term f(t, u, v, w) may be singular at t = 0 and t = 1. The main ingredient is Leray-Schauder nonlinear alternative. 展开更多
关键词 singular ordinary differential equation boundary value problem existence theorem nonlinear alternative
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Existence of Multiple Positive Solutions for Fourth Order Two-point Boundary Value Problems 被引量:1
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作者 戚仕硕 《Northeastern Mathematical Journal》 CSCD 2002年第1期63-72,共10页
The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples ... The present paper tackles two-point boundary value problems for fourth-order differential equations as follows:Several existence theorems on multiple positive solutions to the problems are obtained, and some examples are given to show the validity of these results. 展开更多
关键词 existence theorem multiple positive solution fourth-order boundary value problem
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Minimum Cross Fuzzy Entropy Problem, The Existence of Its Solution and Generalized Minimum Cross Fuzzy Entropy Problems 被引量:1
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作者 Aladdin Shamilov Nihal ince 《Journal of Mathematics and System Science》 2016年第8期315-322,共8页
In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem (Minx(F)EntP) and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the ... In the present study we have formulated a Minimum Cross Fuzzy Entropy Problem (Minx(F)EntP) and proposed sufficient conditions for existence of its solution. Mentioned problem can be formulated as follows. In the set of membership functions satisfying the given moment constraints generated by given moment functions it is required to choose the membership function that is closest to a priori membership function in the sense of cross fuzzy entropy measure. The existence of solution of formulated problem is proved by virtue of concavity property of cross fuzzy entropy measure, the implicit function theorem and Lagrange multipliers method. Moreover, Generalized Cross Fuzzy Entropy Optimization Methods in the form of MinMinx(F)EntM and MaxMinx(F)EntM are suggested on the basis of primary phase of minimizing cross fuzzy entropy measure for fixed moment vector function and on the definition of the special functional with Minx(F)Ent values of cross fuzzy entropy measure. Next phase for obtaining mentioned distributions consists of optimization of defined functional with respect to moment vector functions. Distributions obtained by mentioned methods are defined as (MinMinx(F)Ent)m and (MaxMinx(F)Ent)m distributions. 展开更多
关键词 Cross fuzzy entropy measure Generalized fuzzy entropy optimization problem existence theorem
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EXISTENCE OF SOLUTIONS TO DIFFERENTIALINCLUSIONS IN BANACH SPACES
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作者 宋福民 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1998年第11期0-0,0-0+0-0+0-0+0-0+0,共11页
In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations be... In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces . First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end ,the existence theorem of solutions to differential inclusions is obtained. 展开更多
关键词 Banach space differential inclusion set-valued mappings existence theorem
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Existence of Solutions for a Multi-point Boundary Value Problems with Three Dimension Kernal at Resonance
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作者 LIANG Ju-hua REN Li-shun ZHAO Zhi-liang 《Chinese Quarterly Journal of Mathematics》 CSCD 2011年第1期138-143,共6页
In this paper,a multi-point boundary value problems for a three order nonlinear deferential equation is considered.With the help of coincidence theorem due to Mawhin,a existence theorem is obtained.
关键词 boundary value problems coincidence degree theorem existence theorem 2000 MR Subject Classification:34B10 34B15
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Existence of an Asymptotic Second-order Three-point Boundary Value Problem
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作者 江秀芬 姚庆六 《Northeastern Mathematical Journal》 CSCD 2003年第2期123-126,共4页
By making use of degree theory, a new existence theorem is established for an asymptotic second-order three-point boundary value problem.
关键词 second-order asymptotic equation three-point boundaxy value problem existence theorem
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A NEW INTEGRAL TRANSFORM AND ITS APPLICATIONS
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作者 H.M.SRIVASTAVA 罗旻杰 R.K.RAINA 《Acta Mathematica Scientia》 SCIE CSCD 2015年第6期1386-1400,共15页
In the present paper, the authors introduce a new integral transform which yields a number of potentially useful (known or new) integral transfoms as its special cases. Many fundamental results about this new integr... In the present paper, the authors introduce a new integral transform which yields a number of potentially useful (known or new) integral transfoms as its special cases. Many fundamental results about this new integral transform, which are established in this paper, in- clude (for example) existence theorem, Parseval-type relationship and inversion formula. The relationship between the new integral transform with the H-function and the H-transform are characterized by means of some integral identities. The introduced transform is also used to find solution to a certain differential equation. Some illustrative examples are also given. 展开更多
关键词 Laplace transform Sumudu transform natural transform H-FUNCTION H- transform inversion formula Parseval-type relationship existence theorem Borel-Dzrbashjan transform Fubini's theorem Weierstrass's test Heaviside generalized function
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AN EXTREMUM THEORY OF THE RESIDUAL FUNCTIONAL IN SOBOLEV SPACES W^(m,p)(Ω)
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作者 Ling Yong-yong 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1992年第3期273-279,共7页
In the present paper the concept and properties of the residual functional in Sobolev space are investigated.The weak compactness,force condition,lower semi-continuity and convex of the residual functional are proved.... In the present paper the concept and properties of the residual functional in Sobolev space are investigated.The weak compactness,force condition,lower semi-continuity and convex of the residual functional are proved.In Sobolev space,the minimum principle of the residual functional is proposed.The minimum existence theoreomfor J(u)=0 is given by the modern critical point theory.And the equivalence theorem or five equivalence forms for the residual functional equation are also proved. 展开更多
关键词 Sobolev spaces residual functional infinite Banach spaces CONVEX lower semi-continuity force condition minimum existence theorem
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FIfth-ORDER ISOTROPIC DESCARTES TENSOR
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作者 阎大桂 徐军 +1 位作者 严尚安 付诗禄 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第4期395-398,共4页
Fifth-order isotropic descartes tensor and its existence theorem and representation problems are researched, then a general representation formula of fifth-order isotropic descartes tensor is got.
关键词 descartes tensor isotropic tensor existence theorem representation theorem structure theorem
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Nonlinear Riemann-Hilbert Problem for the First Order Elliptic System with the General Form
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作者 Mingzhong (School of Sciences,Shanghai University) 《Advances in Manufacturing》 SCIE CAS 1999年第2期11-15,共5页
Nonlinear boundary problem for a class of the first order elliptic partial differential system with the general form are studied in this paper.And the equivalent nonlinear singular integral equations are established.T... Nonlinear boundary problem for a class of the first order elliptic partial differential system with the general form are studied in this paper.And the equivalent nonlinear singular integral equations are established.Then the existence theorem of solution of the problem are also obtained. 展开更多
关键词 nonlinear boundary problem integral solution existence theorem
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Non-E_2 Class of Strongly Nonlinear Generalised R-H Boundary Value Problems for Second-Order Elliptic System
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作者 Li Mingzhong Xu Dinghua (College of Sciences) 《Advances in Manufacturing》 SCIE CAS 1998年第3期3-11,共9页
In this paper, a class of strongly non linear generalised Riemann Hilbert problems for second order elliptic system is studied. By means of the theory of integral equations and using an explicit form of the solutio... In this paper, a class of strongly non linear generalised Riemann Hilbert problems for second order elliptic system is studied. By means of the theory of integral equations and using an explicit form of the solution, a reduction is made to a nonlinear boundary value problem for two holomorphic functions. And using an approximation dealing with a solvable perturbed problems and suitable prior estimates, we prove that the problems possess solution in Hardy class, the solution w(z) belongs to W 1 2()∩W 2 p(G),p>2 . 展开更多
关键词 nonlinear boundary value problems perturbed method priori estimation existence theorem
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Algorithm of solutions for generalized nonlinear implicit quasivariational inclusions with fuzzy mappings
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作者 胡学刚 《Journal of Chongqing University》 CAS 2006年第1期36-41,共6页
A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and... A class of generalized implicit quasivariational inclusions with fuzzy mappings in Hilbert space is discussed in this paper which proves an existence theorem of the solutions and proposes a new iterative algorithm and the convergence of the iterative sequence generated by the new algorithm. These results extend and improve some recent corresponding achievements. 展开更多
关键词 generalized nonlinear implicit quasivariational inclusion with fuzzy mappings existence theorem of solutions ITERATIVE
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Potential Method in the Theory of Thermoelasticity with Microtemperatures for Microstretch Solids
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作者 Merab Svanadze Antonio Scalia 《Transactions of Nanjing University of Aeronautics and Astronautics》 EI 2014年第2期159-163,共5页
The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are gi... The linear equilibrium theory of thermoelasticity with microtemperatures for microstretch solids is considered.The basic internal and external boundary value problems(BVPs)are formulated and uniqueness theorems are given.The single-layer and double-layer thermoelastic potentials are constructed and their basic properties are established.The integral representation of general solutions is obtained.The existence of regular solutions of the BVPs is proved by means of the potential method(boundary integral method)and the theory of singular integral equations. 展开更多
关键词 thermoelasticity with microtemperatures existence and uniqueness theorems microstretch solids
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A new class of generalized quasi-variational inequalities with applications to Oseen problems under nonsmooth boundary conditions
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作者 Shengda Zeng Akhtar A.Khan Stanislaw Migórski 《Science China Mathematics》 SCIE CSCD 2024年第2期315-338,共24页
In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the ... In this paper, we study a generalized quasi-variational inequality (GQVI for short) with twomultivalued operators and two bifunctions in a Banach space setting. A coupling of the Tychonov fixedpoint principle and the Katutani-Ky Fan theorem for multivalued maps is employed to prove a new existencetheorem for the GQVI. We also study a nonlinear optimal control problem driven by the GQVI and givesufficient conditions ensuring the existence of an optimal control. Finally, we illustrate the applicability of thetheoretical results in the study of a complicated Oseen problem for non-Newtonian fluids with a nonmonotone andmultivalued slip boundary condition (i.e., a generalized friction constitutive law), a generalized leak boundarycondition, a unilateral contact condition of Signorini’s type and an implicit obstacle effect, in which themultivalued slip boundary condition is described by the generalized Clarke subgradient, and the leak boundarycondition is formulated by the convex subdifferential operator for a convex superpotential. 展开更多
关键词 generalized quasi-variational inequality existence theorem optimal control Kakutani-Ky Fan theorem Oseen problem non-Newtonian fluid nonmonotone slip boundary condition
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A Generalized Existence Theorem of Backward Doubly Stochastic Differential Equations 被引量:7
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作者 Qian LIN 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第8期1525-1534,共10页
In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations (BDSDEs). We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.
关键词 Backward doubly stochastic differential equations comparison theorem existence theorem backward stochastic integral
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COMPARISON THEOREMS TO BOUNDARY VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL EQUATIONS
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作者 LI YONG WANG HUAIZHONG(Department of Matehematics,Jilin University, Changchun 130023, Jilin, China) 《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1994年第2期165-172,共8页
A unified approach is given to several classes of nonlinear boundary value problems, and some previous existence theorems are extended.
关键词 Boundary value problem existence theorem Brouwer degree Schauder's fixed point theorem.
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Existence Theorem of Solutions for Mixed Variational Inequality in Banach Spaces
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作者 Qing Bang ZHANG Liu LIU 《Journal of Mathematical Research and Exposition》 CSCD 2010年第2期323-328,共6页
By using the property of generalized f-projection operator and FKKM theorem, the existence theorem of solutions for the mixed variational inequality is proved under weaker assumption in reflexive and smooth Banach spa... By using the property of generalized f-projection operator and FKKM theorem, the existence theorem of solutions for the mixed variational inequality is proved under weaker assumption in reflexive and smooth Banach space. The results improve and extend the corresponding results shown recentlv. 展开更多
关键词 mixed variational inequality generalized f-projection operator existence theorem FKKM theorem.
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Inequalities and Separation for a Biharmonic Laplace-Beltrami Differential Operator in a Hilbert Space Associated with the Existence and Uniqueness Theorem
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作者 ZAYED E. M. E. 《Journal of Partial Differential Equations》 CSCD 2016年第1期59-70,共12页
In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu(x) = -△△u(x) + V(x)u(x),for all x ∈ R^n, in the Hilbert space H = L2(R^n,H1) with the operator po... In this paper, we have studied the separation for the biharmonic Laplace-Beltrami differential operatorAu(x) = -△△u(x) + V(x)u(x),for all x ∈ R^n, in the Hilbert space H = L2(R^n,H1) with the operator potential V(x) ∈ C^1 (R^n, L (H1) ), where L (H1 ) is the space of all bounded linear operators on the Hilbert space H1, while AAu is the biharmonic differential operator and△u=-∑i,j=1^n 1/√detg δ/δxi[√detgg-1(x)δu/δxj]is the Laplace-Beltrami differential operator in R^n. Here g(x) = (gij(x)) is the Riemannian matrix, while g^-1 (x) is the inverse of the matrix g(x). Moreover, we have studied the existence and uniqueness Theorem for the solution of the non-homogeneous biharmonic Laplace-Beltrami differential equation Au = - △△u + V(x) u (x) = f(x) in the Hilbert space H where f(x) ∈ H as an application of the separation approach. 展开更多
关键词 Separation biharmonic Laplace-Beltrami operator operator potential Hilbert space L2 (R^n H1) coercive estimate existence and uniqueness Theorem.
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