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

Author(s)

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

Affiliation

^[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

• Document type: Journal article
• Source: Rocky Mountain Journal of Mathematics; v. 51, n. 1, p. 243-263, FEB 2021.
• Web of Science Citations: 0

Abstract

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)

• FAPESP's process: 19/24901-3 - Critical nonlocal quasilinear problem: existence, multiplicity and properties of the solutions
• Grantee: Olimpio Hiroshi Miyagaki
• Support Opportunities: Regular Research Grants