Affiliation:
1. Departamento de Matemática Universidade Federal da Paraíba João Pessoa PB Brazil
Abstract
This paper deals with an improvement of a class of Adams type inequalities involving potentials
and weights
, which can decay to zero at infinity as
,
, and
,
, respectively. As an application of this result and by using minimax methods, we establish the existence of solutions for the following class of problems:
where the nonlinear term
can have critical exponential growth. Furthermore, when
we prove that the solutions belong to the Sobolev space
(bound state solutions).
Funder
Conselho Nacional de Desenvolvimento Científico e Tecnológico
Fundação de Apoio à Pesquisa do Estado da Paraíba
Subject
General Engineering,General Mathematics
Reference58 articles.
1. Some estimates connected with integral operators and with solutions of elliptic equations;Yudovich V. I.;Dok. Akad. Nauk. SSSR,1961
2. S. I.Pohozaev The Sobolev embedding in the casepl=n$$ pl=n $$ Proceedings of the Technical Scientific Conference on Advances of Scientific Research 1964‐1965. Math. Section Moscov. Energet. Inst. 1965 pp.158–170.
3. Espaces d'interpolation et théorème de Soboleff
4. On embedding into Orlicz spaces and some applications;Trudinger N. S.;J. Math. Mech.,1967