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arXiv · 1802.03194

Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition

Dušan D. Repovš
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Abstract

We study the degenerate elliptic equation $-\mathop{\rm div}(|x|^\alpha\nabla u) =f(u)+t\phi(x)+h(x)$ in a bounded open set $\Omega$ with homogeneous Neumann boundary condition, where $\alpha\in(0,2)$ and $f$ has a linear growth. The main result establishes the existence of real numbers $t_*$ and $t^*$ such that the problem has at least two solutions if $t\leq t_*$, there is at least one solution if $t_* t^*$. The proof combines a priori estimates with topological degree arguments.

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Dušan D. Repovš. 2018-02-09. Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition. https://arxiv.org/abs/1802.03194

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