arXiv Open Access 2025

Quasilinear Equations with Neumann Boundary Conditions

Annamaria Canino Simone Mauro

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Abstrak

We prove a multiplicity result for non-constant weak solutions $u \in H^1(Ω)$ for the quasilinear elliptic equation \[ \begin{cases} \displaystyle-\text{div}(A(x,u)\nabla u) + \frac{1}{2} D_sA(x,u)\nabla u \cdot \nabla u = g(x,u) - λu & \text{in } Ω\\ A(x,u)\nabla u \cdot η= 0 & \text{on } \partial Ω\end{cases} \] where $λ\in \mathbb{R}$, $ Ω$ is a bounded lipschitz domain, $ η$ is the outward normal to the boundary $ \partial Ω$, and $g(x,u)$ is a Carathéodory function that satisfies a general subcritical (and superlinear) growth condition. We also prove that any weak solution is bounded under a stronger growth assumption.

Topik & Kata Kunci

math.AP

Penulis (2)

Annamaria Canino

Simone Mauro

Format Sitasi

APA MLA BibTeX

Canino, A., Mauro, S. (2025). Quasilinear Equations with Neumann Boundary Conditions. https://arxiv.org/abs/2510.17374

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Informasi Jurnal

Tahun Terbit: 2025
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓