By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations wit...By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.展开更多
In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results a...In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.展开更多
In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the unif...In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.展开更多
In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″...In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.展开更多
Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v...Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v′(1)=v′'′(1)=0,v(0)=∫10 g1(T)v(T)dT,v′′(0)=∫10 g2(T)v′′(T)dT}are obtained,where f,g1,g2 are all continuous.It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs.Moreover,some examples are also included to demonstrate our results as applications.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
This paper deals with the existence of positive solutions to a singular fourth order coupled system with integral boundary conditions. Since the nonlinear terms f, g may change sign or be singular at t = 0 or t = 1, t...This paper deals with the existence of positive solutions to a singular fourth order coupled system with integral boundary conditions. Since the nonlinear terms f, g may change sign or be singular at t = 0 or t = 1, the authors make a priori estimates to overcome some difficulties and apply Cuo-Krasnoselskii fixed point theorem to prove the existence of solutions of the system under suitable assumptions. Finally, some examples to illustrate the main results are given.展开更多
We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed...We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.展开更多
In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=...In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=(1/λ2-1/λ1)∫01q(s)f(s,u(s),u″(s))ds with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem,where f∈C([0,1]×[0,+∞)×(-∞,0],[0,+∞)),q(t)∈L1[0,1]is nonnegative,α,β∈R and satisfyβ<2π2,α>0,α/π4+β/π2<1,λ1,2=(-β+√β^2+4a)/2.The corresponding examples are raised to demonstrate the results we obtained.展开更多
In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem...In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem. Nonlinear term may be singular at t= 0 and/or t - 1 and x =0.展开更多
The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.
基金SuppoSed by the NSF of Anhui Provincial Education Depaxtment(KJ2012A265,KJ2012B187)
文摘By using cone theory and the Monch fixed theorem combined with a monotone iterative technique,we investigate the existence of positive solutions for systems of secondorder nonlinear singular differential equations with integral boundary conditions on infinite interval and establish the existence theorem of positive solutions and iterative sequence for approximating the positive solutions.The results in this paper improve some known results.
文摘In this paper, we study a boundary value problem of nonlinear fractional dif- ferential equations of order q (1 〈 q 〈 2) with non-separated integral boundary conditions. Some new existence and uniqueness results are obtained by using some standard fixed point theorems and Leray-Schauder degree theory. Some illustrative examples are also presented. We extend previous results even in the integer case q = 2.
基金supported by the National Natural Science Foundation of China (Grant No.10701023)and the E-Institutes of Shanghai Municipal Education Commission (Grant No.E03004)
文摘In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.
基金supported by the National Natural Science Foundation of China(No.12071491)。
文摘In this paper,we consider the one dimensional third order p-Laplacian equation(Фp(u″))′+h(t)f(t,u(t))=0 with integral boundary conditions u(0)-αu′(0)=∫_(0)^(1) g1(s)u(s)ds,u(1)+βu′(1)=∫_(0)^(1)g2(s)u(s)ds,u″(0)=0.By using kernel functions and the Avery-Peterson fixed point theorem,we establish the existence of at least three positive solutions.
文摘Based on the Guo-Krasnoselskii’s fixed-point theorem,the existence and multiplicity of positive solutions to a boundary value problem(BVP)with two integral boundary conditions{v(4)=f(s,v(s),v′(s),v〞(s)),s∈[0,1],v′(1)=v′'′(1)=0,v(0)=∫10 g1(T)v(T)dT,v′′(0)=∫10 g2(T)v′′(T)dT}are obtained,where f,g1,g2 are all continuous.It generalizes the results of one positive solution to multiplicity and improves some results for integral BVPs.Moreover,some examples are also included to demonstrate our results as applications.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金The under-graduation base items (J0630104, J0730104, J1030101) of School of Mathematics, Jilin Universitythe 985 program of Jilin University
文摘This paper deals with the existence of positive solutions to a singular fourth order coupled system with integral boundary conditions. Since the nonlinear terms f, g may change sign or be singular at t = 0 or t = 1, the authors make a priori estimates to overcome some difficulties and apply Cuo-Krasnoselskii fixed point theorem to prove the existence of solutions of the system under suitable assumptions. Finally, some examples to illustrate the main results are given.
文摘We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet BCs.The construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the Darboux-dressing process.Under the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector solitons.Connection of our construction to the inverse scattering transform is also provided.
文摘In this paper,the existence and multiplicity of positive solutions for a class of non-resonant fourth-order integral boundary value problem{u(4)(t)+βu″(t)-au(t)=f(t,u(t),u″(t)),t∈(0,1),u″(0)=u″(1)=0,u(0)=0,u(1)=(1/λ2-1/λ1)∫01q(s)f(s,u(s),u″(s))ds with two parameters are established by using the Guo-Krasnoselskii's fixedpoint theorem,where f∈C([0,1]×[0,+∞)×(-∞,0],[0,+∞)),q(t)∈L1[0,1]is nonnegative,α,β∈R and satisfyβ<2π2,α>0,α/π4+β/π2<1,λ1,2=(-β+√β^2+4a)/2.The corresponding examples are raised to demonstrate the results we obtained.
基金Supported by the National Natural Science Foundation of China (Grant No. 10971179)the Natural Science Foundation of Liaocheng University (Grant No. 31805)
文摘In this paper, we investigate the existence of positive solutions for singular fourthorder integral boundary-value problem with p-Laplacian operator by using the upper and lower solution method and fixed point theorem. Nonlinear term may be singular at t= 0 and/or t - 1 and x =0.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘The paper deals a fractional functional boundary value problems with integral boundary conditions. Besed on the coincidence degree theory, some existence criteria of solutions at resonance are established.