JournalsrsmupVol. 143pp. 113–134

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

  • Duong Trong Luyen

    Ton Duc Thang University, Ho Chi Minh City, Vietnam
Sign-changing solutions of boundary value problems for semilinear $\Delta_{\gamma}$-Laplace equations cover
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Abstract

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

{Gαu=g(x,y,u)+f(x,y,u)in Ω,u=0on Ω,\begin{cases} -G_\alpha u= g(x,y,u) + f(x,y,u) & \text{in } \Omega, u= 0 & \text{on } \partial \Omega, \end{cases}

where Ω\Omega is a bounded domain with smooth boundary in RN (N2),αN,g(x,y,ξ),f(x,y,ξ)\mathbb{R}^N \ (N \ge 2), \alpha \in \mathbb{N}, g(x,y,\xi), f(x,y,\xi) are Carathéodory functions and GαG_\alpha 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 Δγ\Delta_{\gamma}-Laplace equations. Rend. Sem. Mat. Univ. Padova 143 (2020), pp. 113–134

DOI 10.4171/RSMUP/42