带有双临界项的薛定谔-泊松系统非平凡解的存在性

Abstract

Abstract:

The existence of a nontrivial solution to the Schrödinger-Poisson type system with both nonlinear critical growth and nonlocal critical growth is obtained by applying the concentration-compactness principle and mountain pass theorem. The double critical growth in the system presents an obstacle when showing the convergence of the bounded (PS) sequences. At the same time, it is difficult to estimate the critical level of the mountain pass. The key ingredient of the paper is to show that the critical level of the mountain pass is below the non-compactness level of the associated energy functional.

Key words: Schrödinger-Poisson type system, Critical exponent, Variational method

CLC Number:

O175.2

Xiaojing Feng. Nontrivial Solution for Schrödinger-Poisson type Systems with Double Critical Terms[J].Acta mathematica scientia,Series A, 2020, 40(6): 1590-1598.

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References 29

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Nontrivial Solution for Schrödinger-Poisson type Systems with Double Critical Terms

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