Existence of ground state solutions for asymptotically linear Schrödinger–Poisson systems
Copyright policy )Existence of ground state solutions for asymptotically linear Schrödinger–Poisson systems
In this paper, we study the following Schrödinger–Poisson system: urn:x-wiley:mma:media:mma3777:mma3777-math-0001 where λ > 0 is a parameter, with 2≤p≤+∞, and the function f(x,s) may not be superlinear in s near zero and is asymptotically linear with respect to s at infinity. Under certain assumptions on V, K, and f, we give the existence and nonexistence results via variational methods. More precisely, when p∈[2,+∞), we obtain that system (SP) has a positive ground state solution for λ small; when p =+ ∞, we prove that system (SP) has a positive solution for λ small and has no any nontrivial solution for λ large. Copyright © 2015 John Wiley & Sons, Ltd.
- Nanjing Normal University China (People's Republic of)
- Nanjing Normal University China (People's Republic of)
- Southeast University China (People's Republic of)
ground state solution, Second-order elliptic systems, asymptotically linear, Positive solutions to PDEs, Variational methods for elliptic systems, variational method, Schrödinger-Poisson system
ground state solution, Second-order elliptic systems, asymptotically linear, Positive solutions to PDEs, Variational methods for elliptic systems, variational method, Schrödinger-Poisson system
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