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Existence and multiplicity of solutions for equations of p(x)-laplace type in rN without AR-condition

Title
Existence and multiplicity of solutions for equations of p(x)-laplace type in rN without AR-condition
Authors
Kim J.-M.Kim Y.-H.Lee J.
Ewha Authors
이종락
Issue Date
2018
Journal Title
Differential and Integral Equations
ISSN
0893-4983JCR Link
Citation
vol. 31, no. 43226.0, pp. 435 - 464
Publisher
Khayyam Publishing
Indexed
SCIE; SCOPUS scopus
Abstract
We are concerned with the following elliptic equations with variable exponents −div(ϕ(x,∇u)) + V(x)

u

p(x)−2u = λf(x,u) in RN, where the function ϕ(x,v) is of type

v

p(x)−2v with continuous function p : RN → (1,∞), V : RN → (0,∞) is a continuous potential function, and f : RN×R → R satisfies a Carathéodory condition. The aims of this paper are stated as follows. First, under suitable assumptions, we show the existence of at least one nontrivial weak solution and infinitely many weak solutions for the problem without the Ambrosetti and Rabinowitz condition, by applying mountain pass theorem and fountain theorem. Second, we determine the precise positive interval of λ’s for which our problem admits a nontrivial solution with simple assumptions in some sense. © 2018 Khayyam Publishing. All Rights Reserved.
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연구기관 > 수리과학연구소 > Journal papers
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