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 - critical point

KW - Ekeland's variational principle

KW - Mountain Pass theorem

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 -