In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(...In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.展开更多
Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with co...Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with constraint.展开更多
Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinea...Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Some results in the literature are improved.展开更多
In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png"...In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.展开更多
The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schr<span st...The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schr<span style="white-space:nowrap;">ö</span>dinger-Poisson equation. We consider a class of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation with variable potential under weaker conditions in this paper. By introducing some new techniques and using truncated functional, Hardy inequality and Poho<span style="white-space:nowrap;"><span style="white-space:nowrap;">ž</span></span>aev identity, we obtain an existence result of a least energy sign-changing solution and a ground state solution for this kind of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation. Moreover, the energy of the sign-changing solution is strictly greater than the ground state energy.展开更多
In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice ...In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.展开更多
In this paper, we discuss the existence of sign-changing solution, positive solution and negative solution to two-point boundary value problem of dynamic equations on measure chains using the cone theory and the fixed...In this paper, we discuss the existence of sign-changing solution, positive solution and negative solution to two-point boundary value problem of dynamic equations on measure chains using the cone theory and the fixed-point index method. The results are different from the previous results.展开更多
基金Supported by the Foundation of the Office of Science and Technology of Henan(122102310373)Supported by the NSF of Education Department of Henan Province(12B110025)
文摘In this paper, by using the fixed-point index theory, we study the existence of sign-changing solution of some three-point boundary value problems {y ''(t) + f(y) = 0, t ∈ [0, 1], y' (0) = 0, y(1) = αy(η), where 0 < α < 1, 0 < η < 1, f : R → R is continuous, strictly increasing and f(0) = 0.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10161010)a fund from Fujian Provincial Education Bureau(Grant No.JA02160).
文摘Via construction of pseudo gradient vector field and descending flow argument, we prove the existence of one positive, one negative and one sign-changing solutions for a quasilinear elliptic eigenvalue problem with constraint.
文摘Using invariant sets of descending flow and variational methods, we establish some sufficient conditions on the existence of sign-changing solutions, positive solutions and negative solutions for second-order nonlinear difference equations with Dirichlet boundary value problem. Some results in the literature are improved.
文摘In this paper we investigate a class of impulsive differential equations with Dirichlet boundary conditions. Firstly, we define new inner product of <img src="Edit_890fce38-e82b-4f36-be40-9d05e8119b88.png" width="40" height="17" alt="" /> and prove that the norm which is deduced by the inner product is equivalent to the usual norm. Secondly, we construct the lower and upper solutions of (1.1). Thirdly, we obtain the existence of a positive solution, a negative solution and a sign-changing solution by using critical point theory and variational methods. Finally, an example is presented to illustrate the application of our main result.
文摘The nodal solutions of equations are considered to be more difficult than the positive solutions and the ground state solutions. Based on this, this paper intends to study nodal solutions for a kind of Schr<span style="white-space:nowrap;">ö</span>dinger-Poisson equation. We consider a class of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation with variable potential under weaker conditions in this paper. By introducing some new techniques and using truncated functional, Hardy inequality and Poho<span style="white-space:nowrap;"><span style="white-space:nowrap;">ž</span></span>aev identity, we obtain an existence result of a least energy sign-changing solution and a ground state solution for this kind of Schr<span style="white-space:nowrap;"><span style="white-space:nowrap;">ö</span></span>dinger-Poisson equation. Moreover, the energy of the sign-changing solution is strictly greater than the ground state energy.
基金Natural Science Foundation of China(10771128)Natural Science Foundation of Shanxi Province(2008011002-1)+2 种基金University Science and Technology Development Project of Shanxi Province(2009744260)Higher Education Teaching Reform Re-Search Project of Shanxi Province(2009744 260)Scientific Research Project of Shanxi Datong University(2010-B-01)
基金Supported in part by the National Natural Science Foundation of China under Grant No.11571207Research Award Fund for Outstanding Young Scientists of Shandong Province under Grant No.BS2012SF022
文摘In this paper, we investigate the existence of nontrivial solutions for some superlinear second order three-point boundary value problems by applying new fixed point theorems in ordered Banach spaces with the lattice structure derived by Sun and Liu.
基金Supported by the National Natural Science Foundation of China (10971179)Natural Science Foundation of Shandong Province (ZR2010AM035)Research Award Fund for Outstanding Young Scientists of Shandong Province (BS2012SF022, BS2010SF023)
文摘In this paper, we discuss the existence of sign-changing solution, positive solution and negative solution to two-point boundary value problem of dynamic equations on measure chains using the cone theory and the fixed-point index method. The results are different from the previous results.
