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1.
In this paper we prove some new existence results of nontrivial solutions for classes of elliptic resonant problems. We also establish several multiplicity results. The methods used here are based on combining the minimax methods and the Morse theory especially some new observations on the critical groups of a local linking-type degenerate critical point.  相似文献   

2.
In this paper, existence of nontrivial solutions for a nonlinear discrete elliptic equation with periodic boundary conditions is considered by using the monotone operator principle, Mountain pass lemma, Linking theorem and some results in Morse theory. The obtained results are also valid and new for the corresponding difference periodic boundary value problem.  相似文献   

3.
苏加宝  李永青 《数学学报》2000,43(6):1135-114
本文应用Morse理论和惩罚性技巧研究了一类半线性椭圆方程在无穷远处和在原点处都共振情形下非平凡解的存在性.  相似文献   

4.
In this paper we study the multiplicity of nontrivial solutions of semilinear elliptic boundary value problems which may be double resonance near infinity between two consecutive eigenvalues of −Δ with zero Dirichlet boundary data. The methods we use here are Morse theory, minimax methods and bifurcation theory.  相似文献   

5.
In this paper several new multiplicity results for asymptotically linear elliptic problem at resonance are obtained via Morse theory and minimax methods. Some new observations on the critical groups of a local linking-type critical point are used to deal with the resonance case at 0.  相似文献   

6.
In this paper, we study the existence of multiple solutions for boundary value problems of second-order difference equations with resonance at both infinity and zero by using Morse theory, critical point theory, minimax methods and bifurcation theory.  相似文献   

7.
In this paper we prove new existence results concerning nontrivial solutions to semilinear elliptic problem at resonance. The methods used here are based on combining the minimax methods and the Morse theory.  相似文献   

8.
In this paper, the existence and multiplicity of a class of double resonant semilinear elliptic equations with the Dirichlet boundary value are studied.  相似文献   

9.
We establish the existence of a nontrivial solution for a class of noncooperative elliptic systems with nonlinearities of superlinear growth. Moreover, if there is resonance, we also find at least a solution. All results are obtained by the minimax methods in critical point theory.  相似文献   

10.
王剑侠  周展 《应用数学》2007,20(2):415-420
本文研究了如下问题:-div(|x|β△u)=|x|^a|u|^2(α,β)-2u+λ|x|σ|u|^q-2,x∈Ω,u=0,x∈δΩ,这里Ω∪→R^N是有界光滑区域且0∈Ω,2(α,β)=2(N+α)/N+β-2,运用Sobolev-Hardy不等式和山路几何,证明了在一定的条件下方程至少存在一个非平凡解。  相似文献   

11.
In this paper, we study the existence of nontrivial solutions for a class of second-order difference equations with multiple resonance at both infinity and the origin by applying the critical point theory and Morse theory.  相似文献   

12.
We consider the semilinear elliptic problem in Ω, u=0 on ∂Ω, where 0∈Ω is a smooth bounded domain in RN, N?4, , is the critical Sobolev exponent, f(x,⋅) has subcritical growth at infinity, K(x)>0 is continuous. We prove the existence of sign-changing solutions under different assumptions when Ω is a usual domain and a symmetric domain, respectively.  相似文献   

13.
By a sub-supersolution method and a perturbed argument, we improve the earlier results concerning the existence of ground state solutions to a semilinear elliptic problem −Δu+p(x)q|∇u|=f(x,u), u>0, xRN, , where q∈(1,2], for some α∈(0,1), p(x)?0, ∀xRN, and f:RN×(0,∞)→[0,∞) is a locally Hölder continuous function which may be singular at zero.  相似文献   

14.
15.
For an even functional on a Banach space, the symmetric mountain pass lemma gives a sequence of critical values which converges to zero. Under the same assumptions on the functional, this paper establishes a new critical point theorem which provides a sequence of critical points converging to zero. The theorem is applied to sublinear elliptic equations. Then a sequence of solutions converging to zero is obtained.  相似文献   

16.
    
This paper is devoted to the existence of solutions for a singular critical semilinear elliptic equation. Some existence and multiplicity results are obtained by using mountain pass arguments and analysis techniques. The results of Ding and Tang (2007) and Kang (2007) and related are improved.  相似文献   

17.
We study the sublinear elliptic equation, −Δ u = |u|psgn u + f(x,u) in the bounded domain Ω under the zero Dirichlet boundary condition. We suppose that 0 < p < 1 and |f(x,u)| is small enough near u = 0 and do not suppose that f(x,u) is odd on u. Then we prove that this problem has infinitely many solutions. Supported in part by the Grant-in-Aid for Scientific Research (C) (No. 16540179), Ministry of Education, Culture, Sports, Science and Technology.  相似文献   

18.
一种奇异临界椭圆方程的非平凡解   总被引:5,自引:0,他引:5       下载免费PDF全文
该文研究了一类带有Sobolev-Hardy临界指数的半线性椭圆方程,运用变分理论中的环绕定理证明了方程非平凡解的存在性  相似文献   

19.
We obtain nonconstant solutions of semilinear elliptic Neumann boundary value problems with jumping nonlinearities when the asymptotic limits of the nonlinearity fall in the type (Il), l>2 and (IIl), l?1 regions formed by the curves of the Fucik spectrum. Furthermore, we have at least two nonconstant solutions in every order interval under resonance case. In this paper, we apply the sub-sup solution method, Fucik spectrum, mountain pass theorem in order intervals, degree theory and Morse theory to get the conclusions.  相似文献   

20.
In this paper the existence of nontrivial periodic solution for second order asymptotically linear difference equation at resonance is obtained. The methods used here are based on combining the minimax methods and the Morse theory, especially the observation on the critical groups.  相似文献   

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