Ground state solutions for quasilinear scalar field equations arising in nonlinear optics

Abstract

In this paper, we study a class of quasilinear elliptic equations which appears in nonlinear optics. By using the mountain pass theorem together with a technique of adding one dimension of space, we prove the existence of a non-trivial weak solution for general nonlinear terms of Berestycki-Lions' type. The existence of a radial ground state solution and a ground state solution is also established under stronger assumptions on the quasilinear term.

25 pages

References in corpus (2)

• On the symmetry of minimizers
• Quasilinear elliptic equations in $\RN$ via variational methods and Orlicz-Sobolev embeddings