共查询到20条相似文献,搜索用时 15 毫秒
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Let us consider the quasilinear problem
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In this paper we consider radially symmetric solutions of the nonlinear Dirichlet problem Δu+f(|x|,u)=0 in Ω, where Ω is a ball in RN, N?3 and f satisfies some appropriate assumptions. We prove existence of radially symmetric solutions with k prescribed number of zeros. Moreover, when f(|x|,u)=K(|x|)|u|p−1u, using the uniqueness result due to Tanaka (2008) [21], we verify that these solutions are non-degenerate and we prove that their radial Morse index is exactly k. 相似文献
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Leiga Zhao Anran LiJiabao Su 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):2520-2533
In this paper, we study a class of quasilinear elliptic exterior problems with nonlinear boundary conditions. Existence of ground states and multiplicity results are obtained via variational methods. 相似文献
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Nikolaos S. Papageorgiou 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(17):6487-6498
We consider a semilinear Neumann problem with an asymptotically linear reaction term. We assume that resonance occurs at infinity. Using variational methods based on the critical point theory, together with the reduction technique and Morse theory, we show that the problem has at least four nontrivial smooth solutions. 相似文献
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Gabriele Bonanno Giovanni Molica Bisci Vicenţiu D. Rădulescu 《Nonlinear Analysis: Theory, Methods & Applications》2012
In this paper, we are interested in the existence of infinitely many weak solutions for a non-homogeneous eigenvalue Dirichlet problem. By using variational methods, in an appropriate Orlicz–Sobolev setting, we determine intervals of parameters such that our problem admits either a sequence of non-negative weak solutions strongly converging to zero provided that the non-linearity has a suitable behaviour at zero or an unbounded sequence of non-negative weak solutions if a similar behaviour occurs at infinity. 相似文献
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Gabriele Bonanno Giovanni Molica Bisci 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(14):4785-4795
The aim of this paper is to establish a multiplicity result for an eigenvalue non-homogeneous Neumann problem which involves a nonlinearity fulfilling a nonstandard growth condition. Precisely, a recent critical points result for differentiable functionals is exploited in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three weak solutions in an appropriate Orlicz-Sobolev space. 相似文献
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Sami Aouaoui 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(4):1843-1858
In the present paper, we are concerned with some degenerate quasilinear equations involving variable exponents. Using various (variational and nonvariational) techniques, we prove existence, nonexistence and multiplicity results. 相似文献
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Dumitru Motreanu 《Journal of Differential Equations》2010,249(12):3352-3376
By variational methods, we prove the existence of a sign-changing solution for the p-Laplacian equation under Dirichlet boundary condition with jumping nonlinearity having relation to the Fu?ík spectrum of p-Laplacian. We also provide the multiple existence results for the p-Laplacian problems. 相似文献
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Liang Zhao 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):433-443
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Radu Precup 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(2):834-851
We obtain critical point variants of the compression fixed point theorem in cones of Krasnoselskii. Critical points are localized in a set defined by means of two norms. In applications to semilinear elliptic boundary value problems this makes possible the use of local Moser-Harnack inequalities for the estimations from below. Multiple solutions are found for problems with oscillating nonlinearity. 相似文献
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In this paper, we consider the problem (Pε) : Δ2u=un+4/n-4+εu,u>0 in Ω,u=Δu=0 on ∂Ω, where Ω is a bounded and smooth domain in Rn,n>8 and ε>0. We analyze the asymptotic behavior of solutions of (Pε) which are minimizing for the Sobolev inequality as ε→0 and we prove existence of solutions to (Pε) which blow up and concentrate around a critical point of the Robin's function. Finally, we show that for ε small, (Pε) has at least as many solutions as the Ljusternik–Schnirelman category of Ω. 相似文献
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Everaldo Medeiros Kyril Tintarev 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(5):2170-2177
We establish some multiplicity results for a class of boundary value problems involving the Hardy-Sobolev operator using Morse theory. 相似文献
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Vicen?iu R?dulescu Dušan Repovš 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(1):99-748
We establish existence results of Hartmann-Stampacchia type for a class of variational-hemivariational inequalities on closed and convex sets (either bounded or unbounded) in a Hilbert space. 相似文献
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We study the existence of nontrivial radial solutions for quasilinear elliptic equations with unbounded or decaying radial potentials. The existence results are based upon several new embedding theorems we establish in the paper for radially symmetric functions. 相似文献
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In this paper, we study the existence of infinitely many nontrivial solutions for a class of semilinear elliptic equations −△u+a(x)u=g(x,u) in a bounded smooth domain of RN(N≥3) with the Dirichlet boundary value, where the primitive of the nonlinearity g is of superquadratic growth near infinity in u and the potential a is allowed to be sign-changing. Recent results in the literature are generalized and significantly improved. 相似文献
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