Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866910690736865280 |
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| author | Amoroso, Eleonora Crespo-Blanco, Ángel Pucci, Patrizia Winkert, Patrick |
| author_facet | Amoroso, Eleonora Crespo-Blanco, Ángel Pucci, Patrizia Winkert, Patrick |
| contents | In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann problems, both of independent interest. Moreover, we study a variable exponent double phase problem with a nonlinear boundary condition and prove the existence of multiple solutions under very general assumptions on the nonlinearities. To be more precise, we get constant sign solutions (nonpositive and nonnegative) via a mountain-pass approach and a sign-changing solution by using an appropriate subset of the corresponding Nehari manifold along with the Brouwer degree and the Quantitative Deformation Lemma. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_17930 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition Amoroso, Eleonora Crespo-Blanco, Ángel Pucci, Patrizia Winkert, Patrick Analysis of PDEs In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness of the solutions of a wide class of nonlinear Neumann problems, both of independent interest. Moreover, we study a variable exponent double phase problem with a nonlinear boundary condition and prove the existence of multiple solutions under very general assumptions on the nonlinearities. To be more precise, we get constant sign solutions (nonpositive and nonnegative) via a mountain-pass approach and a sign-changing solution by using an appropriate subset of the corresponding Nehari manifold along with the Brouwer degree and the Quantitative Deformation Lemma. |
| title | Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2305.17930 |