Abstract
We study the multiplicity of solutions for a class of Hamiltonian systems with the -Laplacian. Under suitable assumptions, we obtain a sequence of solutions associated with a sequence of positive energies going toward infinity.
Highlights
Introduction and Main ResultsSince the space Lp x and W1,p x were thoroughly studied by Kovacik and Rakosnık 1, variable exponent Sobolev spaces have been used in the last decades to model various phenomena
In 7, De Figueiredo and Ding discussed the multiple solutions for a kind of elliptic systems on a smooth bounded domain
−div ∇v p x −2∇v |v|p x −2v −Hv x, u, v, x ∈ Ω, 1.1 u x v x 0, x ∈ ∂Ω, where Ω ⊂ RN is a bounded domain, p is continuous on Ω and satisfies 1 < p− ≤ p x ≤ p < N, and H : Ω × R2 → R is a C1 function
Summary
We study the multiplicity of solutions for a class of Hamiltonian systems with the p x -Laplacian. We obtain a sequence of solutions associated with a sequence of positive energies going toward infinity.
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