Multi-bump solutions for a class of quasilinear problems involving variable exponents

2014/02/27 by Claudianor O. Alves, Alves, Claudianor O., Marcelo C. Ferreira +1
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1402.6838

openalex publication_date 2014/02/27 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28

Abstract

We establish the existence of multi-bump solutions for the following class of quasilinear problems - Δ _p(x) u + ( λV(x) + Z(x) ) u ^p(x)-1 = f(x,u) in \mathbb R^N, u ≥ 0 in \mathbb R^N, where the nonlinearity f \colon \mathbb R^N × \mathbb R → \mathbb R is a continuous function having a subcritical growth and potentials V, Z \colon \mathbb R^N → \mathbb R are continuous functions verifying some hypotheses. The main tool used is the variational method.

Related

• Existence of multi-bump solutions for a class of elliptic problems\n involving the biharmonic operator
• Multi-bump solutions for a Kirchhoff problem type
• Multiplicity of multi-bump type nodal solutions for a class of elliptic problems with exponential critical growth in ℝ²
• Existence of solutions for a class of p(x)-laplacian equations involving a concave-convex nonlinearity with critical growth in ℝ^N
• Existence of multi-bump solutions to biharmonic operator with critical exponential growth in ℝ⁴