Multiplicity of solutions for biharmonic equations with critical exponent and prescribed singularity
Abstract
In this article, we study the singular critical biharmonic problem $$\displaylines \Delta^2u-\mu V(x)u=|u|^{2^*-2}u+\lambda f(x) \quad \text{in } \Omega, \\ u= \frac{\partial u}{\partial n}=0 \quad \text{on } \partial \Omega, }$$ where \( \Delta^2\) is the biharmonic operator, \(\Omega\) is an open bounded domain in \(\mathbb{R}^N\) \((N \geq 5)\) with smooth boundary \(\partial \Omega, 2^* = \frac{2N}{N-4}\), \(0 < \mu < \bar{\mu} := \big( \frac{N(N-4)}{4} \big)^2\), \(f(x)\) and \(V(x)\) are given functions. By using variational method and Nehari-type constraint, we establish the existence of multiple solutions for this problem when \(0
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Electronic Journal of Differential Equations
- Volume
- 2026
- Issue
- 01-??
- Pages
- 02–02
- Publication date
- 8 January 2026