Existence and multiplicity of solutions for nonlinear Dirac-Poisson systems

Date

2017-03-29

Authors

Zhang, Jian
Zhang, Wen
Tang, Xianhua

Journal Title

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Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

This article concerns the nonlinear Dirac-Poisson system -i ∑3k=1 αk∂ku + (V(x) + α) βu + ωu - φu = Fu(x, u), -∆φ = 4π|u|2, in ℝ3, where V(x) is a potential function and F(x, u) is an asymptotically quadratic nonlinearity modeling various types of interaction. Since the effects of the nonlocal term, we use some special techniques to deal with the nonlocal term. Moreover, the existence of infinitely many stationary solutions is obtained for system with periodicity assumption via variational methods.

Description

Keywords

Dirac-Poisson system, Asymptotically quadratic, Variational methods, Strongly indefinite functionals

Citation

Zhang, J., Zhang, W., & Tang, X. (2017). Existence and multiplicity of solutions for nonlinear Dirac-Poisson systems. <i>Electronic Journal of Differential Equations, 2017</i>(91), pp. 1-17.

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Attribution 4.0 International

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