Existence of solutions for nonlinear equations with mixed local and nonlocal operators
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915646487396352 |
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| author | Iannizzotto, Antonio |
| author_facet | Iannizzotto, Antonio |
| contents | We study an elliptic equation, with homogeneous Dirichlet boundary conditions, driven by a mixed type operator (the sum of the Laplacian and the fractional Laplacian), involving a parametric reaction and an undetermined source term. Applying a recent abstract critical point theorem of Ricceri, we prove existence of a solution for a convenient source and small enough parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_22620 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of solutions for nonlinear equations with mixed local and nonlocal operators Iannizzotto, Antonio Analysis of PDEs 35R11, 35A15 We study an elliptic equation, with homogeneous Dirichlet boundary conditions, driven by a mixed type operator (the sum of the Laplacian and the fractional Laplacian), involving a parametric reaction and an undetermined source term. Applying a recent abstract critical point theorem of Ricceri, we prove existence of a solution for a convenient source and small enough parameters. |
| title | Existence of solutions for nonlinear equations with mixed local and nonlocal operators |
| topic | Analysis of PDEs 35R11, 35A15 |
| url | https://arxiv.org/abs/2511.22620 |