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

Alessio Pomponio; Tatsuya Watanabe

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arXiv · 2004.04957

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

Alessio Pomponio·Tatsuya Watanabe

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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.

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Alessio Pomponio, Tatsuya Watanabe. 2020-04-10. Ground state solutions for quasilinear scalar field equations arising in nonlinear optics. https://arxiv.org/abs/2004.04957

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