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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.15825 |
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| _version_ | 1866913460578680832 |
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| author | Zongo, Emmanuel Wend-Benedo Feulefack, Pierre Aime |
| author_facet | Zongo, Emmanuel Wend-Benedo Feulefack, Pierre Aime |
| contents | We investigate a nonlinear nonlocal eigenvalue problem involving the sum of fractional $(p,q)$-Laplace operators $(-Δ)_p^{s_1}+(-Δ)_q^{s_2}$ with $s_1,s_2\in (0,1)$; $p,q\in(1,\infty)$ and subject to Dirichlet boundary conditions in an open bounded set of $\mathbb{R}^N$. We prove bifurcation results from trivial solutions and from infinity for the considered nonlinear nonlocal eigenvalue problem. We also show the existence of multiple solutions of the nonlinear nonlocal problem using variational methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_15825 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bifurcation results and multiple solutions for the fractional $(p,q)$-Laplace operators Zongo, Emmanuel Wend-Benedo Feulefack, Pierre Aime Analysis of PDEs Nonlocal operators, nonlinear eigenvalue values, bifurcation results, critical point theory, fractional $(p, q)$-Laplacian, multiple solutions We investigate a nonlinear nonlocal eigenvalue problem involving the sum of fractional $(p,q)$-Laplace operators $(-Δ)_p^{s_1}+(-Δ)_q^{s_2}$ with $s_1,s_2\in (0,1)$; $p,q\in(1,\infty)$ and subject to Dirichlet boundary conditions in an open bounded set of $\mathbb{R}^N$. We prove bifurcation results from trivial solutions and from infinity for the considered nonlinear nonlocal eigenvalue problem. We also show the existence of multiple solutions of the nonlinear nonlocal problem using variational methods. |
| title | Bifurcation results and multiple solutions for the fractional $(p,q)$-Laplace operators |
| topic | Analysis of PDEs Nonlocal operators, nonlinear eigenvalue values, bifurcation results, critical point theory, fractional $(p, q)$-Laplacian, multiple solutions |
| url | https://arxiv.org/abs/2406.15825 |