共查询到20条相似文献,搜索用时 31 毫秒
1.
Dumitru Motreanu 《Journal of Differential Equations》2007,232(1):1-35
In this paper we examine semilinear and nonlinear Neumann problems with a nonsmooth locally Lipschitz potential function. Using variational methods based on the nonsmooth critical point theory, for the semilinear problem we prove a multiplicity result under conditions of double resonance at higher eigenvalues. Our proof involves a nonsmooth extension of the reduction method due to Castro-Lazer-Thews. The nonlinear problem is driven by the p-Laplacian. So first we make some observations about the beginning of the spectrum of (−Δp,W1,p(Z)). Then we prove an existence and multiplicity result. The existence result permits complete double resonance. The multiplicity result specialized in the semilinear case (i.e. p=2) corresponds to the super-sub quadratic situation. 相似文献
2.
Michael E. Filippakis Nikolaos S. Papageorgiou Vasile Staicu 《Nonlinear Analysis: Theory, Methods & Applications》2008
In this paper we study eigenvalue problems for hemivariational and variational inequalities driven by the p-Laplacian differential operator. Using topological methods (based on multivalued versions of the Leray–Schauder alternative principle) and variational methods (based on the nonsmooth critical point theory), we prove existence and multiplicity results for the eigenvalue problems that we examine. 相似文献
3.
In this paper we consider two nonlinear elliptic problems driven by the p-Laplacian and having a nonsmooth potential (hemivariational inequalities). The first is an eigenvalue problem and we prove
that if the parameter λ < λ2 = the second eigenvalue of the p-Laplacian, then there exists a nontrivial smooth solution. The second problem is resonant both near zero and near infinity
for the principal eigenvalue of the p-Laplacian. For this problem we prove a multiplicity result. Our approach is variational based on the nonsmooth critical point
theory.
Second author is Corresponding author. 相似文献
4.
In this paper we establish a multiplicity theorem for critical points of
functionals on reflexive Banach spaces. Precisely, we deduce the main result
using a general variational principle proved by Ricceri. Moreover,
we present an application to a Neumann problem which gives a
positive answer to some questions formulated by the previous
author.Received: 6 February 2003 相似文献
5.
Everaldo Medeiros 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):3654-3660
In this paper we study a quasilinear elliptic problem with the Dirichlet boundary condition in a bounded domain involving the operator Au=−Δpu−Δqu. Assuming that the nonlinearity has a concave-convex behavior we obtain some multiplicity results. More precisely, we obtain five nontrivial solutions; two by a minimization argument, two by the mountain pass theorem, and the other by a cohomological linking theorem. 相似文献
6.
Antonio Iannizzotto Nikolaos S. Papageorgiou 《Nonlinear Analysis: Theory, Methods & Applications》2009
In this paper we consider a nonlinear Neumann problem driven by the p-Laplacian with a nonsmooth potential (hemivariational inequality). Using minimax methods based on the nonsmooth critical point theory together with suitable truncation techniques, we show that the problem has at least three nontrivial smooth solutions. Two of these solutions have constant sign (one is positive, the other negative). 相似文献
7.
In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We
also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The
second is for systems and it is based on the nonsmooth local linking theorem. 相似文献
8.
In this paper we study nonlinear periodic systems driven by the ordinary p-Laplacian with a nonsmooth potential. We prove an existence theorem using a nonsmooth variant of the reduction method. We also prove two multiplicity results. The first is for scalar problems and uses the nonsmooth second deformation lemma. The second is for systems and it is based on the nonsmooth local linking theorem. 相似文献
9.
In this work we improve some known results for a singular operator and also for a wide class of lower-order terms by proving a multiplicity result. The proof is made by applying the generalized mountain-pass theorem due to Ambrosetti and Rabinowitz. To do this, we show that the minimax levels are in a convenient range by combining a special class of approximating functions, due to Gazzola and Ruf, with the concentrating functions of the best Sobolev constant. 相似文献
10.
A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. 相似文献
11.
In this paper we prove some existence results of semilinear Dirichlet problems in nonsmooth domains in presence of lower and upper solutions well-ordered or not. We first prove existence results in an abstract setting using degree theory. We secondly apply them for domains with conical points. 相似文献
12.
We consider a nonlinear elliptic problem driven by a nonlinear nonhomogeneous differential operator and a nonsmooth potential. We prove two multiplicity theorems for problems with coercive energy functional. In both theorems we produce three nontrivial smooth solutions. In the second multiplicity theorem, we provide precise sign information for all three solutions (the first positive, the second negative and the third nodal). Out approach is variational, based on the nonsmooth critical point theory. We also prove an auxiliary result relating smooth and Sobolev local minimizer for a large class of locally Lipschitz functionals. 相似文献
13.
We study the multiplicity of critical points for functionals which are only differentiable along some directions. We extend to this class of functionals the three critical point theorem of Pucci and Serrin and we apply it to a one-parameter family of functionals Jλ, λ∈I⊂R. Under suitable assumptions, we locate an open subinterval of values λ in I for which Jλ possesses at least three critical points. Applications to quasilinear boundary value problems are also given. 相似文献
14.
In this paper we consider nonlinear periodic systems driven by the ordinary p-Laplacian and having a nonsmooth potential function. Under minimal and natural hypotheses on the nonsmooth potential and using variational methods based on the nonsmooth critical point theory we prove four existence theorems and a multiplicity theorem. We conclude the paper with an existence theorem for the scalar problem, in which the energy functional is indefinite (i.e. it is unbounded both above and below). 相似文献
15.
We study a nonlinear eigenvalue problem with a nonsmooth potential. The subgradients of the potential are only positive near
the origin (from above) and near +∞. Also the subdifferential is not necessarily monotone (i.e. the potential is not convex).
Using variational techniques and the method of upper and lower solutions, we establish the existence of at least two strictly
positive smooth solutions for all the parameters in an interval. Our approach uses the nonsmooth critical point theory for
locally Lipschitz functions. A byproduct of our analysis is a generalization of a result of Brezis-Nirenberg (CRAS, 317 (1993))
on H10 versus C10 minimizers of a C1-functional. 相似文献
16.
In this paper we consider a nonlinear eigenvalue problem driven by the p-Laplacian differential operator and with a nonsmooth potential. Using degree theoretic arguments based on the degree map for certain operators of monotone type, we show that the problem has at least two nontrivial positive solutions as the parameter λ>0 varies in a half-line. 相似文献
17.
Shiwang Ma 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(12):3856-3872
In this paper, we consider a class of resonant cooperative elliptic systems. Based on some new results concerning the computations of the critical groups and the Morse theory, we establish some new results about the existence and multiplicity of solutions under new classes of conditions. It turns out that our main results sharply improve some known results in the literature. 相似文献
18.
Dengfeng Lü 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6371-6382
In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic systems with Sobolev critical exponent in a bounded domain. By using the variational method and the Nehari manifold, we obtain the existence and multiplicity results of nontrivial solutions for the systems. 相似文献
19.
Chengfu Wang Yisheng Huang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):4076-4081
In this paper, using nonsmooth critical point theory, we study the existence of multiple solutions of the following class of problems:
20.
In this paper we study a nonlinear second order periodic problem driven by a scalar p ‐Laplacian and with a nonsmooth, locally Lipschitz potential function. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of nontrivial positive solutions and then establish the existence of a second distinct solution (multiplicity theorem) by strengthening further the hypotheses. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献