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Sign-changing solutions of boundary value problems for semilinear Δγ​-Laplace equations

Authors: 

Duong Trong Luyen

Source title: 
Rendiconti del Seminario Matematico della Universita di Padova, 143: 113-134, 2020 (ISI)
Academic year of acceptance: 
2020-2021
Abstract: 

In this article, we study the multiplicity of weak solutions to the boundary value problem

{-Gα​u = g(x, y, u) + f(x, y, u) in Ω, u = 0 on ∂Ω,​

whereΩ is a bounded domain with smooth boundary in a\ (N ≥ 2), α ∈ a, g(x, y, ξ), f(x, y, ξ) are Carathéodory functions and Gα​ is the Grushin operator. We use the lower bounds of eigenvalues and an abstract theory on sign-changing solutions.