Sebastián Lorca

Nonexistence of Positive Solution for Quasilinear Elliptic Problems in the Half-Space

Liouville-type results in or in the half-space might be important to obtain a priori estimates for positive solutions of associated problems in bounded domains via some procedure of blow up. In this work, we obtain a nonexistence result for the positive solution of, in the half-space.

Multiplicity of solutions for a class of non-homogeneous fourth-order boundary value problems

We study the multiplicity of positive solutions for a class of fourth-order boundary value problems with non-homogeneous boundary conditions. For this, we use a fixed point theorem of cone expansion/compression type and we establish a general theorem for a type of systems of second-order ordinary differential equations involving parameters. In addition, we apply our result to the study of the existence of solutions for semilinear elliptic systems in bounded annular domains.

Existence and Multiplicity Results for Degenerate Elliptic Equations with Dependence on the Gradient

We study the existence of positive solutions for a class of degenerate nonlinear elliptic equations with gradient dependence. For this purpose, we combine a blowup argument, the strong maximum principle, and Liouville-type theorems to obtain a priori estimates.

Multiparameter Elliptic Equations in Annular Domains

Using fixed point theorems of cone expansion/compression type, the upper-lower solutions method and degree arguments, we study existence, non-existence and multiplicity of positive solutions for a class of second-order ordinary differential equations with multiparameters. We apply our results to semilinear elliptic equations in bounded annular domains with non-homogeneous Dirichlet boundary conditions. More precisely, we apply our main results to equations of the form

Existence of Solutions to Quasilinear Elliptic Equations With Singular Weights

\begin{array}{*{20}c} \begin{gathered} - \Delta u \hfill \\ u\left( x \right) \hfill \\ u\left( x \right) \hfill \\ \end{gathered} & \begin{gathered} = \hfill \\ = \hfill \\ = \hfill \\ \end{gathered} & \begin{gathered} \lambda f\left( {\left| x \right|,u} \right) \hfill \\ a \hfill \\ b \hfill \\ \end{gathered} \\ \end{array} \begin{array}{*{20}c} \begin{gathered} in \hfill \\ on \hfill \\ on \hfill \\ \end{gathered} & \begin{gathered} r_1 < \left| x \right| < r_{2,} \hfill \\ \left| x \right| = r_1 , \hfill \\ \left| x \right| = r_2 , \hfill \\ \end{gathered} \\ \end{array}

POSITIVE SOLUTIONS TO A NON-RADIAL SUPERCRITICAL KLEIN–GORDON-TYPE EQUATION

, where a, b and λ are non-negative parameters. One feature of the hypotheses on the nonlinearities that we consider is that they have some sort of local character.

Positive solutions for certain classes of fourth-order ordinary elliptic systems

In this paper we study the existence and multiplicity of positive radial solutions for a class of semilinear elliptic systems in bounded annular domains with non-homogeneous boundary conditions by the use of a fixed-point theorem of cone expansion/compression type.

Free boundary solutions to a log-singular elliptic equation

Abstract In this paper we show the existence of multiple solutions to a class of quasilinear elliptic equations with singular weights when the continuous nonlinearity satisfies a superlinear condition only at zero. In particular, our approach allows us to consider superlinear, critical and supercritical nonlinearities.