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Infinitely Many Solutions for Semilinear Strongly Degenerate Elliptic Differential Equations with Lack of Symmetry

Authors: 

Duong Trong Luyen

Source title: 
Acta Applicandae Mathematicae, 175: 3, 2021 (ISI)
Academic year of acceptance: 
2021-2022
Abstract: 

In this paper, we study the existence of multiple solutions for the boundary value problem

a

where ΩΩ is a bounded domain with smooth boundary in a, where a is odd, a is a non-symmetric, perturbative term and ΔγΔγ is the strongly degenerate elliptic operator of the type

a

By using a perturbation method introduced by Bolle (J. Differ. Equ. 152:274-288, 1999), we prove the existence of multiple solutions in spite of the lack of symmetry of the problem.