Ground state solutions for Hamiltonian elliptic system with sign-changing potential
Date
2017-07-04
Authors
Zhang, Wen
Xie, Xiaoliang
Mi, Heilong
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the Hamiltonian elliptic system
-∆u + V(x)u = Hv(x, u, v), x ∈ ℝN,
-∆v + V(x)v = Hu(x, u, v), x ∈ ℝN,
u(x) → 0, v(x) → 0, as |x| → ∞,
where z = (u, v) : ℝN → ℝ x ℝ, N ≥ 3 and the potential V(x) is allowed to be sign-changing. Under the weak superquadratic assumptions for the nonlinearities, by applying the variant generalized weak linking theorem for strongly indefinite problem developed by Schechter and Zou, we obtain the existence of nontrivial and ground state solutions.
Description
Keywords
Hamiltonian elliptic system, Superquadratic, Sign-changing potential, Generalized weak linking theorem
Citation
Zhang, W., Xie, X., & Mi, H. (2017). Ground state solutions for Hamiltonian elliptic system with sign-changing potential. Electronic Journal of Differential Equations, 2017(164), pp. 1-13.
Rights
Attribution 4.0 International