共查询到20条相似文献,搜索用时 281 毫秒
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We prove the existence of multiple constant-sign and sign-changing solutions for a nonlinear elliptic eigenvalue problem under Dirichlet boundary condition involving the p-Laplacian. More precisely, we establish the existence of a positive solution, of a negative solution, and of a nontrivial sign-changing solution when the eigenvalue parameter λ is greater than the second eigenvalue λ2 of the negative p-Laplacian, extending results by Ambrosetti–Lupo, Ambrosetti–Mancini, and Struwe. Our approach relies on a combined use of variational and topological tools (such as, e.g., critical points, Mountain-Pass theorem, second deformation lemma, variational characterization of the first and second eigenvalue of the p-Laplacian) and comparison arguments for nonlinear differential inequalities. In particular, the existence of extremal nontrivial constant-sign solutions plays an important role in the proof of sign-changing solutions. 相似文献
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We study nonlinear eigenvalue problems for the p-Laplace operator subject to different kinds of boundary conditions on a bounded domain. Using the Ljusternik–Schnirelman principle, we show the existence of a nondecreasing sequence of nonnegative eigenvalues. We prove the simplicity and isolation of the principal eigenvalue and give a characterization for the second eigenvalue. 相似文献
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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
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The aim of this paper is to establish the existence of an unbounded sequence of weak solutions for a class of differential equations with p(x)-Laplacian and subject to small perturbations of nonhomogeneous Neumann conditions. The approach is based on variational methods. 相似文献
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Nikolaos S. Papageorgiou Eugénio M. Rocha Vasile Staicu 《Nonlinear Analysis: Theory, Methods & Applications》2008
We consider a parametric nonlinear elliptic inclusion with a multivalued p-Laplacian-like differential operator and a nonsmooth potential (hemivariational inequality). Using a variational approach based on the nonsmooth critical point theory, we show that for all the values of the parameter in an open half-line, the problem admits at least two nontrivial solutions. Our result extends a recent one by Kristály, Lisei, and Varga [A. Kristály, H. Lisei, C. Varga, Multiple solutions for p-Laplacian type operator, Nonlinear Anal. 68 (5) (2008) 1375–1381]. 相似文献
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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
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In the present paper, a quasilinear elliptic problem with a critical Sobolev exponent and a Hardy-type term is considered. By means of a variational method, the existence of nontrivial solutions for the problem is obtained. The result depends crucially on the parameters p,t,s,λ and μ. 相似文献
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In this paper, we successfully generalize the eigenvalue comparison theorem for the Dirichlet p -Laplacian (1<p<∞) obtained by Matei (2000) [19] and Takeuchi (1998) [22], respectively. Moreover, we use this generalized eigenvalue comparison theorem to get estimates for the first eigenvalue of the Dirichlet p-Laplacian of geodesic balls on complete Riemannian manifolds with radial Ricci curvature bounded from below w.r.t. some point. In the rest of this paper, we derive an upper and lower bound for the heat kernel of geodesic balls of complete manifolds with specified curvature constraints, which can supply new ways to prove the most part of two generalized eigenvalue comparison results given by Freitas, Mao and Salavessa (2013) [9]. 相似文献
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In this paper we give sufficient conditions for the nonexistence of positive entire weak solutions of coercive and anticoercive elliptic inequalities, both of the p-Laplacian and of the mean curvature type, depending also on u and x inside the divergence term, while a gradient factor is included on the right-hand side. In particular, to prove our theorems we use a technique developed by Mitidieri and Pohozaev in [E. Mitidieri, S.I. Pohozaev, A priori estimates and the absence of solutions of nonlinear partial differential equations and inequalities, Proc. Steklov Inst. Math., 234 (2001) 1–362], which relies on the method of test functions without using comparison and maximum principles. Their approach is essentially based first on a priori estimates and on the derivation of an asymptotics for the a priori estimate. Finally nonexistence of a solution is proved by contradiction. 相似文献
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This paper is concerned with the positive solutions for generalized quasilinear Schrödinger equations in RN with critical growth which have appeared from plasma physics, as well as high-power ultrashort laser in matter. By using a change of variables and variational argument, we obtain the existence of positive solutions for the given problem. 相似文献
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Susana Merchán Luigi Montoro Ireneo Peral Berardino Sciunzi 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2014
In this work we deal with the existence and qualitative properties of the solutions to a supercritical problem involving the −Δp(⋅) operator and the Hardy–Leray potential. Assuming 0∈Ω, we study the regularizing effect due to the addition of a first order nonlinear term, which provides the existence of solutions with a breaking of resonance. Once we have proved the existence of a solution, we study the qualitative properties of the solutions such as regularity, monotonicity and symmetry. 相似文献
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