Prescribed energy solutions of concave-convex type problems involving sign-changing or vanishing weights
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914176283181056 |
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| author | Perera, Kanishka Quoirin, Humberto Ramos Silva, Kaye |
| author_facet | Perera, Kanishka Quoirin, Humberto Ramos Silva, Kaye |
| contents | We provide an abstract approach to find couples $(λ,u) \in \mathbb{R} \times X$ satisfying $$Φ_λ(u)=c \quad \mbox{and} \quad Φ'_λ(u)=0,$$ for some suitable values of $c \in \mathbb{R}$. Here $Φ_λ$ is a $C^1$ functional (set on a Banach space $X$) whose main prototype is the energy functional associated to a concave-convex problem with sign-changing or vanishing weights. This approach allows us to derive several existence, multiplicity and bifurcation type results for the equation $Φ'_λ(u)=0$ with $λ$ fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01931 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Prescribed energy solutions of concave-convex type problems involving sign-changing or vanishing weights Perera, Kanishka Quoirin, Humberto Ramos Silva, Kaye Analysis of PDEs We provide an abstract approach to find couples $(λ,u) \in \mathbb{R} \times X$ satisfying $$Φ_λ(u)=c \quad \mbox{and} \quad Φ'_λ(u)=0,$$ for some suitable values of $c \in \mathbb{R}$. Here $Φ_λ$ is a $C^1$ functional (set on a Banach space $X$) whose main prototype is the energy functional associated to a concave-convex problem with sign-changing or vanishing weights. This approach allows us to derive several existence, multiplicity and bifurcation type results for the equation $Φ'_λ(u)=0$ with $λ$ fixed. |
| title | Prescribed energy solutions of concave-convex type problems involving sign-changing or vanishing weights |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2512.01931 |