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 (Hirata et al. in Topol Methods Nonlinear Anal 35:253–276, 2010; Jeanjean in Nonlinear Anal Theory Methods Appl 28:1633–1659, 1997), 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.

中文翻译：

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非线性光学中拟线性标量场方程的基态解

在本文中，我们研究了一类出现在非线性光学中的拟线性椭圆方程。通过使用山口定理和增加一维空间的技术（Hirata等人在Topol Methods Nonlinear Anal 35：253–276，2010; Jeanjean in Nonlinear Anal Theory Methods Appl 28：1633-1659，1997）中，我们证明了Berestycki–Lions型广义非线性项的非平凡弱解的存在。在拟线性项的更强假设下，还建立了径向基态解和基态解的存在。