A study of the nonlocal solution of p-Laplacian fractional elliptic problems via approximation methods
Abstract In the present paper, we are concerned with the existence of nonnegative solutions for two Kirchhoff-type problems driven by a fractional p-Laplacian operator, ( − Δ ) p s $(-\Delta )_{p}^{s}$ , in a bounded smooth domain Ω of R N $\mathbb{R}^{N}$ with N > p s $N>ps$ . by employing ap...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-12-01
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| Series: | Boundary Value Problems |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13661-024-01981-w |
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| Summary: | Abstract In the present paper, we are concerned with the existence of nonnegative solutions for two Kirchhoff-type problems driven by a fractional p-Laplacian operator, ( − Δ ) p s $(-\Delta )_{p}^{s}$ , in a bounded smooth domain Ω of R N $\mathbb{R}^{N}$ with N > p s $N>ps$ . by employing approximation methods, we establish the existence of nonnegative solutions for each problems under some hypotheses on f , g : Ω × R → R $f,g : \Omega \times \mathbb{R}\to \mathbb{R}$ and weak conditions on the diffusion coefficients M , N : ( 0 , + ∞ ) → R $\mathcal{M}, \mathcal{N} :(0,+\infty )\to \mathbb{R}$ that we will present. The regularity of finite-energy solutions of both problems is also studied by imposing a few extra hypotheses on Ω, f, and g. |
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| ISSN: | 1687-2770 |