Infinitely many solutions for asymptotically linear periodic
Hamiltonian elliptic systems

Fukun Zhao; Leiga Zhao; Yanheng Ding

Displaying similar documents to “Infinitely many solutions for asymptotically linear periodic Hamiltonian elliptic systems”

On the existence of infinitely many solutions for a class of semilinear elliptic equations in $R^{N}$

Francesca Alessio, Paolo Caldiroli, Piero Montecchiari (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We show, by variational methods, that there exists a set $A$ open and dense in $a \in L^{\infty} (R^{N}) : a \geq 0$ such that if $a \in A$ then the problem $- △ u + u = a (x) {|u|}^{p - 1} u, u \in H^{1} (R^{N})$ , with $p$ subcritical (or more general nonlinearities), admits infinitely many solutions.

An elliptic equation with no monotonicity condition on the nonlinearity

Gregory S. Spradlin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

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An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle...

Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains.

Ishiwata, Michinori (2005)

Abstract and Applied Analysis

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A refinement of the radial Pohozaev identity

Florin Catrina (2010)

Mathematica Bohemica

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In this article we produce a refined version of the classical Pohozaev identity in the radial setting. The refined identity is then compared to the original, and possible applications are discussed.

An Campanato type regularity condition for local minimisers in the calculus of variations

Thomas J. Dodd (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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An Campanato type regularity condition is established for a class of WX local minimisers $\bar{u}$ of the general variational integral $\int_{Ω} F (\nabla u (x)) d x$ where $Ω \subset ℝ^{n}$ is an open bounded domain, is of class C, is strongly quasi-convex and satisfies the growth condition $F (ξ) \leq c (1 + | ξ |^{p})$ for a and where the corresponding Banach spaces X are the Morrey-Campanato space $ℒ^{p, μ} (Ω, ℝ^{N \times n})$ , < , Campanato space $ℒ^{p, n} (Ω, ℝ^{N \times n})$ and the space of bounded mean oscillation $BMO Ω, ℝ^{N \times n})$ . The admissible maps $u : Ω \to ℝ^{N}$ are of Sobolev class W, satisfying a Dirichlet boundary condition,...

On critical points for noncoercive functionals and subharmonic solutions of some Hamiltonian systems.

Schmitt, Klaus, Wang, Zhi-Qiang (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Radially symmetric solutions for a class of critical exponent elliptic problems in $ℝ^{N}$ .

Alves, C.O., de Morais Filho, D.C., Souto, M.A.S. (1996)

Electronic Journal of Differential Equations (EJDE) [electronic only]

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Existence and multiplicity of positive solutions to a class of quasilinear elliptic equations in $ℝ^{N}$ .

Hsu, Tsing-San (2010)

Boundary Value Problems [electronic only]

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