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.
Ground state solutions for quasilinear scalar field equations arising in nonlinear optics
Alessio Pomponio;
2021-01-01
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.File in questo prodotto:
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