Multiplicity Results for Mixed Local Nonlocal Equations With Indefinite Concave-Convex Type Nonlinearity
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866913849261686784 |
|---|---|
| author | Dhanya, R. Giacomoni, Jacques Jana, Ritabrata |
| author_facet | Dhanya, R. Giacomoni, Jacques Jana, Ritabrata |
| contents | In this article we examine the multiplicity of non-negative solutions to mixed local-nonlocal equations involving \((-Δ_p) + (-Δ^{s}_{q})\) in a bounded smooth domain. The nonlinearity incorporates a parameter \(λ> 0\), a sublinear term, and a superlinear term, with sign-changing weight functions \(a(x)\) and \(b(x)\). Under suitable conditions, we establish the existence of at least two distinct nontrivial non-negative solutions in both the subcritical and critical regimes via fibering map analysis and constrained minimization on the Nehari manifold. Additionally, for \(p \not = q\), we obtain a nonexistence result for large \(λ\) by analyzing the associated generalized eigenvalue problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiplicity Results for Mixed Local Nonlocal Equations With Indefinite Concave-Convex Type Nonlinearity Dhanya, R. Giacomoni, Jacques Jana, Ritabrata Analysis of PDEs 35J20, 35J25, 35J60, 35J92, 35R11 In this article we examine the multiplicity of non-negative solutions to mixed local-nonlocal equations involving \((-Δ_p) + (-Δ^{s}_{q})\) in a bounded smooth domain. The nonlinearity incorporates a parameter \(λ> 0\), a sublinear term, and a superlinear term, with sign-changing weight functions \(a(x)\) and \(b(x)\). Under suitable conditions, we establish the existence of at least two distinct nontrivial non-negative solutions in both the subcritical and critical regimes via fibering map analysis and constrained minimization on the Nehari manifold. Additionally, for \(p \not = q\), we obtain a nonexistence result for large \(λ\) by analyzing the associated generalized eigenvalue problem. |
| title | Multiplicity Results for Mixed Local Nonlocal Equations With Indefinite Concave-Convex Type Nonlinearity |
| topic | Analysis of PDEs 35J20, 35J25, 35J60, 35J92, 35R11 |
| url | https://arxiv.org/abs/2503.00365 |