TY - JOUR
T1 - Existence and multiplicity of weak solutions for nonuniformly elliptic equations with nonstandard growth condition
AU - Mashiyev, R. A.
AU - Cekic, B.
AU - Avci, M.
AU - Yucedag, Z.
N1 - Funding Information:
The authors thank the referees for their valuable suggestions and helpful corrections, which have improved the presentation of this article. This research project was supported by DUBAP -10-FF-15, Dicle University, Turkey.
PY - 2012/5
Y1 - 2012/5
N2 - We discuss the problem - div(a(x, ∇u)) = m(x){divides}u{divides}r(x)-2u + n(x){divides}u{divides}s(x)-2u in Ω, where Ω is a bounded domain with smooth boundary in ℝN(N ≥ 2), and div(a(x, ∇u)) is a p(x)-Laplace type operator with 1 & r(x) & p(x) & s(x). We show the existence of infinitely many nontrivial weak solutions in. Our approach relies on the theory of the variable exponent Lebesgue and Sobolev spaces combined with adequate variational methods and a variation of the Mountain Pass lemma and critical point theory.
AB - We discuss the problem - div(a(x, ∇u)) = m(x){divides}u{divides}r(x)-2u + n(x){divides}u{divides}s(x)-2u in Ω, where Ω is a bounded domain with smooth boundary in ℝN(N ≥ 2), and div(a(x, ∇u)) is a p(x)-Laplace type operator with 1 & r(x) & p(x) & s(x). We show the existence of infinitely many nontrivial weak solutions in. Our approach relies on the theory of the variable exponent Lebesgue and Sobolev spaces combined with adequate variational methods and a variation of the Mountain Pass lemma and critical point theory.
KW - Ekeland's variational principle
KW - Mountain Pass theorem
KW - critical point
KW - multiple solutions
KW - nonuniform elliptic equations
KW - p(x)-Laplace operator
UR - http://www.scopus.com/inward/record.url?scp=84859620326&partnerID=8YFLogxK
U2 - 10.1080/17476933.2011.598928
DO - 10.1080/17476933.2011.598928
M3 - Journal Article
AN - SCOPUS:84859620326
SN - 1747-6933
VL - 57
SP - 579
EP - 595
JO - Complex Variables and Elliptic Equations
JF - Complex Variables and Elliptic Equations
IS - 5
M1 - 598928
ER -