Existence and multiplicity of solutions for nonlinear Dirac-Poisson systems
Date
2017-03-29
Authors
Zhang, Jian
Zhang, Wen
Tang, Xianhua
Journal Title
Journal ISSN
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.
Rights
Attribution 4.0 International