Existence of solution for a class of variational inequality in whole ℝ^N with critical growth: The local Mountain pass case

2020/11/01 by Claudianor O. Alves, Alves, Claudianor O., Luciano M. Barros +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.2011.00468

openalex publication_date 2020/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study the existence of solution for a class of variational inequality in whole ℝ^N where the nonlinearity has a critical growth for N ≥ 2. By combining a penalization scheme found in del Pino and Felmer [18] with a penalization method due to Bensoussan and Lions [9], we improve a recent result by Alves, Barros and Torres [1].

Related

• Concentration-compactness principle for mountain pass problems
• Existence of solutions for a class of p(x)-laplacian equations involving a concave-convex nonlinearity with critical growth in ℝ^N
• Mountain Passes and Saddle Points
• Existence of solutions for a nonlocal variational problem in ℝ² with exponential critical growth
• Fractional elliptic problems with critical growth in the whole of \Rⁿ