Multiplicity results for elliptic problems with critical exponential growth

2024/01/26 by Kanishka Perera, Perera, Kanishka
Computer Science · Engineering · Mathematics · #58E05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Primary 35J20 #Secondary 35B33 #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2401.15209

openalex publication_date 2024/01/26 · openalex created_date 2024/02/01 · openalex updated_date 2026/07/28

Abstract

We prove new multiplicity results for some elliptic problems with critical exponential growth. More specifically, we show that the problems considered here have arbitrarily many solutions for all sufficiently large values of a certain parameter μ> 0. In particular, the number of solutions goes to infinity as μ→ ∞. The proof is based on an abstract critical point theorem.

Related

• Abstract multiplicity theorems and applications to critical growth problems
• A bifurcation and multiplicity result for a critical growth elliptic problem
• Multiplicity of strong solutions for a class of elliptic problems without the Ambrosetti-Rabinowitz condition in ℝ^N
• Perturbation from symmetry and multiplicity of solutions for elliptic\n problems with subcritical exponential growth in R²
• MULTIPLICITY RESULTS IN THE NON-COERCIVE CASE FOR AN ELLIPTIC PROBLEM WITH CRITICAL GROWTH IN THE GRADIENT