Nontrivial solutions to the Dirichlet problems for semilinear degenerate elliptic equations

2023/03/26 by Duong Trong Luyen, Luyen, Duong Trong, Nguyen Minh Tri +3
Computer Science · Mathematics · #35J40 #35J70 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2303.14661

openalex publication_date 2023/03/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the existence of non-trivial weak solutions for the following boundary-value problem -(∂² u)/(∂ x²) -|x|^2k(∂² u)/(∂ y²)=f(x,y,u) in Ω, u=0 on ∂Ω, where Ω is a bounded domain with smooth boundary in ℝ², Ω∩ \x=0\≠ ∅, k >0, f(x,y,0)=0.

Related

• Semilinear elliptic degenerate equations with critical exponent
• Existence of solutions of degenerate semilinear elliptic boundary value problems
• Existence of Weak Solutions of Linear Subelliptic Dirichlet Problems\n With Rough Coefficients
• Multiplicity of solutions to a degenerate elliptic equation in the sub-critical and critical cases
• Solutions for autonomous semilinear elliptic equations