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Existence of nontrivial weak solutions for a quasilinear Choquard equation
- Existence of nontrivial weak solutions for a quasilinear Choquard equation
- Lee, Jongrak; Kim, Jae-Myoung; Bae, Jung-Hyun; Park, Kisoeb
- Ewha Authors
- Issue Date
- Journal Title
- JOURNAL OF INEQUALITIES AND APPLICATIONS
- Weak solutions; Variational method; Choquard equation
- SPRINGER INTERNATIONAL PUBLISHING AG
- SCIE; SCOPUS
- 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.
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