Existence, concentration and multiplicity of solutions for -Laplacian equations with convolution term
In this paper, we concern some qualitative properties of the following [Formula: see text]-Laplacian equations with convolution term: − Δpu − ΔNu + V (𝜀x)(|u|p−2u + |u|N−2u) = [|x|−μ ∗ F(u)]f(u),x ∈ ℝN,u ∈ W1,p(ℝN) ∩ W1,N(ℝN), x ∈ ℝN, where [Formula: see text] is a positive parameter, [Formula: see...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
World Scientific Publishing
2025-04-01
|
| Series: | Bulletin of Mathematical Sciences |
| Subjects: | |
| Online Access: | https://www.worldscientific.com/doi/10.1142/S1664360724500097 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, we concern some qualitative properties of the following [Formula: see text]-Laplacian equations with convolution term: − Δpu − ΔNu + V (𝜀x)(|u|p−2u + |u|N−2u) = [|x|−μ ∗ F(u)]f(u),x ∈ ℝN,u ∈ W1,p(ℝN) ∩ W1,N(ℝN), x ∈ ℝN, where [Formula: see text] is a positive parameter, [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] satisfies the critical exponential growth. By using the variational methods and the penalization method, we prove the existence of solutions for the above equations which concentrates at a local minimum of V in the semi-classical limit as [Formula: see text]. Moreover, we obtain the multiplicity of solutions for the above equations by the Morse theory. |
|---|---|
| ISSN: | 1664-3607 1664-3615 |