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一类带有对数非线性项的拟线性椭圆方程解的存在性及多重性
Existence and Multiplicity of Solutions for a Class of Quasilinear Elliptic Equations with Logarithmic Nonlinearity

DOI: 10.12677/PM.2022.123044, PP. 400-410

Keywords: 拟线性，弱下半连续，非光滑
Quasilinear, Weak Lower Semicontinuous, Nonsmooth

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Abstract:

本文讨论一类带有对数非线性项的拟线性椭圆方程解的存在性和多重性。对主项系数A(x,t)提出合适的条件，使用弱下半连续泛函的非光滑临界点定理证明该问题存在山路解和无穷多非平凡解。
In this paper, we consider the existence and multiplicity of solutions of a class of quasilinear elliptic equations with logarithmic nonlinearity. Under some appropriate conditions for the principal coefficient A(x,t), we use the nonsmooth critical point theorem of weak lower semicontinuous functional to prove the problem has mountain path solutions and infinite nontrivial solutions.

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