Journal
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
Volume 190, Issue -, Pages -Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.na.2019.111598
Keywords
Variable exponent; Nonlocal Kirchhoff equation; p(x)-Laplacian operator; Palais-Smale condition; Mountain Pass theorem; Fountain theorem
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Funding
- Department of Mathematics, Faculty of Sciences and Arts, King Khalid University, Muhayil Asir
- Slovenian Research Agency [P1-0292, J1-0831, N1-0064, N1-0083, N1-0114]
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In this work, we study the existence and multiplicity results for the following nonlocal p(x)-Kirchhoff problem: { - (a - b integral(Omega) 1/p(x) vertical bar del u vertical bar(p(x)) dx) div (vertical bar del u vertical bar(p(x)-2)del u) = lambda vertical bar u vertical bar(p(x)-2) u + g(x, u) in Omega, (0.1) u = 0, on partial derivative Omega, where a >= b > 0 are constants, Omega subset of R-N is a bounded smooth domain, p is an element of C ((Omega) over bar) with N > p(x) > 1, lambda real parameter and g is a continuous function. The analysis developed in this paper proposes an approach based on the idea of considering a new nonlocal term which presents interesting difficulties. (C) 2019 Elsevier Ltd. All rights reserved.
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