Solitary Waves for a Class of Quasilinear Schrödinger Equations Involving Vanishing Potentials

Autor:	Elisandra Gloss, João Marcos do Ó, Cláudia R. Santana
Rok vydání:	2015
Předmět:	symbols.namesake Class (set theory) General Mathematics Mountain pass theorem symbols Statistical and Nonlinear Physics Schrödinger field Schrödinger equation Mathematical physics Mathematics
Zdroj:	Scopus-Elsevier
ISSN:	2169-0375 1536-1365
DOI:	10.1515/ans-2015-0308
Popis:	In this paper we study the existence of weak positive solutions for the following class of quasilinear Schrödinger equations −Δu + V(x)u − [Δ(u2)]u = h(u) in ℝN, where h satisfies some “mountain-pass” type assumptions and V is a nonnegative continuous function. We are interested specially in the case where the potential V is neither bounded away from zero, nor bounded from above. We give a special attention to the case when V may eventually vanish at infinity. Our arguments are based on penalization techniques, variational methods and Moser iteration scheme.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85ab34cf80bac34671fac6609c1257ac https://doi.org/10.1515/ans-2015-0308 Zobrazit plný text záznamu