Ground state solutions for a class of generalized quasilinear Schrödinger–Poisson systems

Abstract

This paper is concerned with the existence of ground state solutions for a class of generalized quasilinear Schrödinger-Poisson systems in R 3 which have appeared in plasma physics, as well as in the description of high-power ultrashort lasers in matter. By employing a change of variables, the generalized quasilinear systems are reduced to a semilinear one, whose associated functionals are well defined in the usual Sobolev space and satisfy the mountain-pass geometric. Finally, we use Ekeland's variational principle and the mountain-pass theorem to obtain the ground state solutions for the given problem.

Quasilinear asymptotically periodic Schrödinger–Poisson system with subcritical growth

“…The authors in [31] considered a system with radial potentials and discontinuous nonlinearity and obtained multiplicity results for radial solutions. By using Ekeland's variational principle and the mountain pass theorem the authors in [33] obtained the existence of the ground state solution for a generalized quasilinear Schrödinger-Poisson system in R 3 . For related results on nonlinear problems based on variational methods, we refer to [21,28,32,[38][39][40][41][42], which are recent contributions to Kirchhoff-type problems.…”

Ground state solutions of Nehari–Pohožaev type for a kind of nonlinear problem with general nonlinearity and nonlocal convolution term

“…There is also other work about ground state solutions for (1.2); we refer to [20,21]. Motivated by the above work and [22][23][24][25][26][27][28][29][30], in the present paper, we shall extend the results concerning the existence of ground state solutions for (1.2) in [23] to (1.1).…”