Sign-changing solutions of boundary value problems for semilinear $\Delta_{\gamma}$-Laplace equations

Duong Trong Luyen

doi:10.4171/rsmup/42

JournalsrsmupVol. 143pp. 113–134

Sign-changing solutions of boundary value problems for semilinear $Δ_{γ}$ -Laplace equations

Duong Trong Luyen
Ton Duc Thang University, Ho Chi Minh City, Vietnam

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Abstract

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

{- G_{α} u = g (x, y, u) + f (x, y, u) in Ω, u = 0 on \partial Ω,

where $Ω$ is a bounded domain with smooth boundary in $R^{N} (N \geq 2), α \in N, g (x, y, ξ), f (x, y, ξ)$ are Carathéodory functions and $G_{α}$ is the Grushin operator. We use the lower bounds of eigenvalues and an abstract theory on sign-changing solutions.

Cite this article

Duong Trong Luyen, Sign-changing solutions of boundary value problems for semilinear $Δ_{γ}$ -Laplace equations. Rend. Sem. Mat. Univ. Padova 143 (2020), pp. 113–134

DOI 10.4171/RSMUP/42