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Existence of nontrivial weak solutions for a quasilinear Choquard equation

Title
Existence of nontrivial weak solutions for a quasilinear Choquard equation
Authors
Lee, JongrakKim, Jae-MyoungBae, Jung-HyunPark, Kisoeb
Ewha Authors
이종락
Issue Date
2018
Journal Title
JOURNAL OF INEQUALITIES AND APPLICATIONS
ISSN
1029-242XJCR Link
Keywords
Weak solutionsVariational methodChoquard equation
Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
Indexed
SCIE; SCOPUS WOS
Abstract
We are concerned with the following quasilinear Choquard equation: -Delta(p)u + V(x)vertical bar u vertical bar(p-2) u =lambda(I-alpha * F(u))f(u) in R-N, F(t) = integral(t)(0) f(s)ds, 0 f (s) ds, where 1 < p < infinity, Delta(p)u = del . (vertical bar del u vertical bar(p-2) del u) is the p-Laplacian operator, the potential function V : R-N -> (0, infinity) is continuous and F is an element of C-1(R, R). Here, I-alpha : R-N -> R is the Riesz potential of order alpha is an element of(0, p). We study the existence of weak solutions for the problem above via the mountain pass theorem and the fountain theorem. Furthermore, we address the behavior of weak solutions to the problem near the origin under suitable assumptions for the nonlinear term f.
DOI
10.1186/s13660-018-1632-z
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연구기관 > 수리과학연구소 > Journal papers
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