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Existence and multiplicity of solutions for Kirchhoff–Schrödinger type equations involving p(x)-Laplacian on the entire space RN

Title
Existence and multiplicity of solutions for Kirchhoff–Schrödinger type equations involving p(x)-Laplacian on the entire space RN
Authors
Lee J.Kim J.-M.Kim Y.-H.
Ewha Authors
이종락
Issue Date
2019
Journal Title
Nonlinear Analysis: Real World Applications
ISSN
1468-1218JCR Link
Citation
vol. 45, pp. 620 - 649
Keywords
Critical point theoremsp(x)-Kirchhoff-type equationsp(x)-LaplacianVariational methodsWeak solutions
Publisher
Elsevier Ltd
Indexed
SCIE; SCOPUS scopus
Abstract
This study is concerned with the following elliptic equation: −M(∫RN[Formula presented]

∇u

p(x)dx)div(

p(x)−2∇u)+V(x)

u

p(x)−2u=λf(x,u)inRN,where M∈C(R+) is a Kirchhoff-type function, the potential function V:RN→(0,∞) is continuous, and f:RN×R→R satisfies a Carathéodory condition. The aim is to determine the precise positive interval of λ for which the problem admits at least two nontrivial solutions by using abstract critical point results for an energy functional satisfying the Cerami condition. It should be noted that the existence of at least one nontrivial weak solution is established by employing the mountain pass theorem. Moreover, the existence of an unbounded sequence of nontrivial weak solutions follows from the fountain theorem owing to the variational nature of the problem. © 2018 Elsevier Ltd
DOI
10.1016/j.nonrwa.2018.07.016
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연구기관 > 수리과학연구소 > Journal papers
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