| Abstract: |
| In this talk we study the existence of weak solutions of the quasilinear equation
$$
\begin{cases}
-\div (a(|\nabla u|^2)\nabla u)=\lambda f(x,u) &\mbox{in }\Omega,\ u=0 &\mbox{on }\partial\Omega,
\end{cases}
$$
where $a:\mathbb{R}\to [0,\infty)$ is $C^1$ and a nonincreasing continuous function near the origin, the nonlinear term $f:\Omega\times\mathbb{R}\to\mathbb{R}$ is a Carath\`eodory function verifying certain superlinear conditions only at zero, and $\lambda$ is a positive parameter. The existence of the solution relies on $C^1-$estimates and variational arguments. |
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