Skip to content

Feiyan Huang, Chunyu Lei, Changmu Chu, Uniqueness, multiple normalized solutions for p-Laplacian equation with singular growth

Full Text: PDF
DOI: 10.23952/jnva.10.2026.6.07

Volume 10, Issue 6, 1 December 2026, Pages 1163-1200

 

Abstract. In this paper, we consider the existence of normalized solutions for a singular p-Laplacian equation. We derive a local minimizer and a mountain-pass type normalized solution using the concentration-compactness lemma and minimax theorems. Meanwhile, with the help of the truncation technique and genus theory, we establish the existence of infinitely many low-energy solutions. When the critical nonlinearity is replaced with an L^q-supercritical one, we further obtain infinitely many high-energy solutions. Additionally, we investigate the unique normalized solution to a p-Laplacian equation without a critical perturbation term.

 

How to Cite this Article:
F. Huang, C. Lei, C. Chu, Uniqueness, multiple normalized solutions for p-Laplacian equation with singular growth, J. Nonlinear Var. Anal. 10 (2026), 1163-1200.