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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 J.; Kim J.-M.; Bae J.-H.; Park K.
- Ewha Authors
- Issue Date
- Journal Title
- Journal of Inequalities and Applications
- Journal of Inequalities and Applications vol. 2018
- Choquard equation; Variational method; Weak solutions
- Springer International Publishing
- Document Type
- We are concerned with the following quasilinear Choquard equation: −Δpu+V(x)
p−2u=λ(Iα∗F(u))f(u)in RN,F(t)=∫0tf(s)ds,(Formula presented.) where 1 < p< ∞ , Δ pu= ∇ ⋅ (
p − 2∇ u) is the p-Laplacian operator, the potential function V: RN→ (0 , ∞) is continuous and F∈ C1(R, R). Here, Iα: RN→ R is the Riesz potential of order α∈ (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. © 2018, The Author(s).
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