Multiplicity of solutions for a nonlocal nonhomogeneous Neumann boundary problem with two critical exponents

Article type: Research Article

Authors: Costa, Augusto^{a; *} | Pinheiro, Andréia^b

Affiliations: [a] Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará, PA, Brazil | [b] Instituto Federal do Pará, IFPA, PA, Brazil

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: This article concerns the multiplicity of solutions for a class of nonlocal and nonhomogeneous Neumann boundary value problems involving the p(x)-Laplacian, in which both nonlinear terms assume critical growth. We use variational method, exploring an important truncation argument and properties of the genus.

Keywords: Nonlocal problem, Neumann boundary conditions, Sobolev spaces with variable exponent, critical exponent, truncation argument

DOI: 10.3233/ASY-211715

Journal: Asymptotic Analysis, vol. 128, no. 4, pp. 517-538, 2022