It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the ...It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the operator -Δ in the space H 1 0(Ω).展开更多
The purpose of this paper is to study a semilinear Schr<span style="white-space:nowrap;">ö</span>dinger equation with constraint in <em>H</em><sup>1</sup>(<str...The purpose of this paper is to study a semilinear Schr<span style="white-space:nowrap;">ö</span>dinger equation with constraint in <em>H</em><sup>1</sup>(<strong>R</strong><sup><em>N</em></sup>), and prove the existence of sign changing solution. Under suitable conditions, we obtain a negative solution, a positive solution and a sign changing solution by using variational methods.展开更多
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
基金This research is supported by NNSFC(1 9771 0 72 ) and ZNSF.And thanks to JNCASR in India Fortheir host when the firstauthor is
文摘It is proved that the semilinear elliptic problem with zero boundary value -Δ u=λu-|u| q-1 u has a changing sign solution, as q∈(0,1) and λ>λ 2 , where λ 2 is the second eigenvalue of the operator -Δ in the space H 1 0(Ω).
文摘The purpose of this paper is to study a semilinear Schr<span style="white-space:nowrap;">ö</span>dinger equation with constraint in <em>H</em><sup>1</sup>(<strong>R</strong><sup><em>N</em></sup>), and prove the existence of sign changing solution. Under suitable conditions, we obtain a negative solution, a positive solution and a sign changing solution by using variational methods.
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supported by Science and Technology Plan Foundation of Guangdong Province(2006J1-C0341)Science Foundation of the Education Department of Fujian Province(JA06035)~~
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)
