Universidade Federal de São Carlos

Título: Local Coercivity for semilinear elliptic problems

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Conferenciante: José Miguel Mendoza Aranda (Universidade Federal de São Carlos, Brasil)

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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.

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Fecha: 25 de mayo de 2018, 12:00 - 13:00
Lugar: Seminario 1, IEMath-GR

Título: Generalized Nehari manifold and semilinear Schrödinger equation

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Conferenciante: Francisco Odair Vieira de Paiva (Universidade Federal de São Carlos)

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Resumen: We study the Schrödinger equation $−∆u + V (x)u = f (x, u)$ in $\mathbb{R}^N$. We assume that $f$ is superlinear but of subcritical growth and $u → f (x, u)/|u|$ is nondecreasing. We also assume that $V$ and $f$ are periodic in $x_1, . . . , x_N$. We show that these equations have a ground state and that there exist infinitely many solutions if $f$ is odd in $u$.

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20 de octubre de 2016, 13:00, Seminario de Matemáticas de la 1ª planta, Facultad de Ciencias

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Más información sobre el seminario de ecuaciones diferenciales aquí.