Multiple solutions to asymptotically linear problems driven by superposition operators
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915304685174784 |
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| author | Afonso, Danilo Gregorin Bartolo, Rossella Bisci, Giovanni Molica |
| author_facet | Afonso, Danilo Gregorin Bartolo, Rossella Bisci, Giovanni Molica |
| contents | In this paper, we investigate the existence and multiplicity of weak solutions to problems involving a superposition operator of the type $$\int_{[0, 1]}(- Δ)^s u d μ(s),$$ for a signed measure $μ$ on the interval of fractional exponents $[0,1]$, when the nonlinearity is subcritical and asymptotically linear at infinity; thus, we deal with a perturbation of the eigenvalue problem for the superposition operator. We use variational tools, extending to this setting well-known results for the classical and the fractional Laplace operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_10269 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multiple solutions to asymptotically linear problems driven by superposition operators Afonso, Danilo Gregorin Bartolo, Rossella Bisci, Giovanni Molica Analysis of PDEs 35R11, 35A15, 49J35, 35S15, 58E05, 47G20 In this paper, we investigate the existence and multiplicity of weak solutions to problems involving a superposition operator of the type $$\int_{[0, 1]}(- Δ)^s u d μ(s),$$ for a signed measure $μ$ on the interval of fractional exponents $[0,1]$, when the nonlinearity is subcritical and asymptotically linear at infinity; thus, we deal with a perturbation of the eigenvalue problem for the superposition operator. We use variational tools, extending to this setting well-known results for the classical and the fractional Laplace operators. |
| title | Multiple solutions to asymptotically linear problems driven by superposition operators |
| topic | Analysis of PDEs 35R11, 35A15, 49J35, 35S15, 58E05, 47G20 |
| url | https://arxiv.org/abs/2504.10269 |