# Ambrosetti-Prodi problem with degenerate potential and Neumann boundary condition

30 Aug 2019 Repovš Dušan D.

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 $t_*<t\leq t^*$, and no solution exists for all $t>t^*$... (read more)

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