Detalles de Evento
Título: Local Coercivity for semilinear elliptic problems
Conferenciante: José Miguel Mendoza Aranda (Universidade Federal de São Carlos, Brasil)
Resumen: For a bounded domain $\Omega$, a bounded Carathéodory function $g$ in $\Omega \times \mathbb{R}$, $p>1$, a nonnegative integrable function $h$ in $\Omega$ which is strictly positive in a set of positive measure and a continuous function $a$ which is superlinear with polynomial growth we prove that, contrarily with the case $h\equiv 0$, there exists a solution of the semilinear elliptic problem \begin{equation}\label{pa} \left \{ \begin{array}{rcll} -\Delta u & = & \lambda u +g(x,u)- h(x) a(u) +f, & \mbox{in } \Omega \\ u & = & 0, & \mbox{on } \partial\Omega,\\ \end{array} \right. \end{equation} for every $\lambda\in\mathbb{R}$ and $f\in\ L^2(\Omega)$. And also give results of existence and multiplicity of similar problems, such that fractional laplacian problem, homogeneous problem and a concave perturbation of the above problem.
Fecha: 25 de mayo de 2018, 12:00 - 13:00
Lugar: Seminario 1, IEMath-GR
Conferenciante: José Miguel Mendoza Aranda (Universidade Federal de São Carlos, Brasil)
Resumen: For a bounded domain $\Omega$, a bounded Carathéodory function $g$ in $\Omega \times \mathbb{R}$, $p>1$, a nonnegative integrable function $h$ in $\Omega$ which is strictly positive in a set of positive measure and a continuous function $a$ which is superlinear with polynomial growth we prove that, contrarily with the case $h\equiv 0$, there exists a solution of the semilinear elliptic problem \begin{equation}\label{pa} \left \{ \begin{array}{rcll} -\Delta u & = & \lambda u +g(x,u)- h(x) a(u) +f, & \mbox{in } \Omega \\ u & = & 0, & \mbox{on } \partial\Omega,\\ \end{array} \right. \end{equation} for every $\lambda\in\mathbb{R}$ and $f\in\ L^2(\Omega)$. And also give results of existence and multiplicity of similar problems, such that fractional laplacian problem, homogeneous problem and a concave perturbation of the above problem.
Fecha: 25 de mayo de 2018, 12:00 - 13:00
Lugar: Seminario 1, IEMath-GR
