Existence of solutions for logarithmic Kirchhoff equation without compactness in $\mathbb{R}^3$
Abstract
In this paper, we investigate the logarithmic Kirchhoff-type equation - ( a + b ∫ R 3 | ∇ u | 2 d x ) Δ u + V ( x ) u = | u | p - 2 u log | u | , x ∈ R 3 where a , b > 0 are constants, and V : R 3 → R is continuous and may change sign. Using Nehari manifold method and the concentration-compactness principle, we prove the existence of nontrivial and nonnegative (weak) solutions under some assumptions on the potential function V without radial symmetry or compactness hypotheses.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Nonlinear Differential Equations Analysis
Stability and Controllability of Differential Equations
Publication details
- Journal / source
- Electronic journal of qualitative theory of differential equations
- Issue
- 3
- Pages
- 1–22
- Publication date
- 1 January 2026
- Language
- ENG