### Session S02 - Diverse Aspects of Elliptic PDEs and Related Problems

Wednesday, July 21, 18:00 ~ 18:30 UTC-3

## Effect of non-linear lower order terms in quasilinear equations involving the $p(x)$-Laplacian

### Analía Silva

#### UNSL-IMASL, Argentina - This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we study the existence of $W_0^{1, p(x)}$-solutions to the following boundary value problem involving the $p(x)$-Laplacian operator:

$$ \left\lbrace \begin{array}{l} -\Delta_{p(x)}u+|\nabla u|^{q(x)}=\lambda g(x)u^{\eta(x)}+f(x), \quad in \Omega, \\\qquad \,\,\,\,\,\quad \quad\qquad\quad u\geq 0, \quad in \Omega\\ \qquad \,\,\,\,\,\quad \quad\qquad\quad u= 0, \,\,\quad on \partial\Omega.\\ \end{array} \right. $$under appropriate ranges on the variable exponents. We give assumptions on $f$ and $g$ in terms of the growth exponents $q$ and $\eta$ under which the above problem has a solution for all $\lambda > 0$.

Joint work with Pablo Ochoa (UNCUYO).