SCHRODINGER EQUATIONS IN R-4 INVOLVING THE BIHARMONIC OPERATOR WITH CRITICAL EXPONENTIAL GROWTH

Autor(es)

Miyagaki, Olimpio H. ^[1] ; Santana, Claudia R. ^[2] ; Vieira, Ronei S. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Carlos, Ctr Ciencias Exatas & Tecnol, Dept Matemat, Sao Carlos - Brazil

^[2] Univ Estadual Santa Cruz, Dept Ciencias Exatas & Tecnol, Ilheus, BA - Brazil

^[3] Fed Inst Espirito Santo, Licenciatura Matemat, Cachoeiro Do Itapemirim - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Rocky Mountain Journal of Mathematics; v. 51, n. 1, p. 243-263, FEB 2021.
• Citações Web of Science: 0

Resumo

In this paper we prove the existence of at least one nontrivial ground state solution for fourth-order elliptic equations of the form (P) Delta(2)u -Delta u + u =K(x){[}f(u) + g(u)], x epsilon R-4, u epsilon H-2(R-4), where Delta(2)u := Delta(Delta) is the biharmonic operator, f is a continuous nonnegative function with polynomial growth at infinity, g is a continuous nonnegative function with exponential growth and K is a positive bounded continuous function that can vanish at infinity. Our results complete the analysis made in F. Sani (Comm. Pure Appl. Anal. 12 (2013), 405-428), where the author studied Schrodinger equations involving the biharmonic operator with coercive potentials. Our approach is based on various techniques such as the mountain-pass theorem, Trundinger-Moser type inequalities and compactness results. (AU)

• Processo FAPESP: 19/24901-3 - Problema quase linear não local crítica: existência, multiplicidade e propriedades das soluções
• Beneficiário: Olimpio Hiroshi Miyagaki
• Modalidade de apoio: Auxílio à Pesquisa - Regular