Existence and asymptotic behavior of solutions for a class of semilinear subcritical elliptic systems

Article type: Research Article

Authors: Arruda, Suellen Cristina Q.^{a; *} | Figueiredo, Giovany M.^b | Nascimento, Rubia G.^c

Affiliations: [a] Faculdade de Ciências Exatas e Tecnologia, Universidade Federal do Pará – UFPA, CEP: 68440-000, Abaetetuba-PA, Brazil | [b] Departamento de Matemática, Universidade de Brasília – UNB, CEP: 70910-900, Brasília-DF, Brazil | [c] Instituto de Ciências Exatas e Naturais, Universidade Federal do Pará – UFPA, CEP: 66075-110, Belém-PA, Brazil

Correspondence: [*] Corresponding author. E-mail: scqarruda@ufpa.br.

Abstract: In this paper we study the asymptotic behaviour of a family of elliptic systems, as far as the existence of solutions is concerned. We give a special attention to the asymptotic behaviour of W and V as ε goes to zero in the system −ε2Δu+W(x)u=Qu(u,v)in RN,−ε2Δv+V(x)v=Qv(u,v)in RN,u,v∈H1(RN),u(x),v(x)>0for each x∈RN, where ε>0, W and V are positive potentials of C2 class and Q is a p-homogeneous function with subcritical growth. We establish the existence of a positive solution by considering two classes of potentials W and V. Our arguments are based on penalization techniques, variational methods and the Moser iteration scheme.

Keywords: Elliptic system, asymptotic analysis, Palais–Smale condition, positive solution

DOI: 10.3233/ASY-201671

Journal: Asymptotic Analysis, vol. 127, no. 1-2, pp. 15-34, 2022