Artículo

A singular elliptic equation with natural growth in the gradient and a variable exponent

Journal ar
Nonlinear Differential Equations and Applications
  • Volumen: 22
  • Número: 6
  • Fecha: 01 diciembre 2015
  • Páginas: 1935-1948
  • ISSN: 14209004 10219722
  • Tipo de fuente: Revista
  • DOI: 10.1007/s00030-015-0351-0
  • Tipo de documento: Artículo
  • Editorial: Birkhauser Verlag AG
© 2015, Springer Basel. In this paper we consider singular quasilinear elliptic equations with quadratic gradient and a singular term with a variable exponent (Formula presented.) Here ¿ is an open bounded set of RR, ¿(x) is a positive continuous function and f is positive function that belongs to a certain Lebesgue space. We show, among other results, that there exists a solution in the natural energy space H0 1(¿) to this problem when ¿(x) is strictly less than 2 in a strip around the boundary; while there is no solution in the energy space when there exists(Formula presented.) with (Formula presented.) such that ¿(x)>2 on ¿. Moreover, since we work by approximation we can analyze the behavior of the approximated solutions un in the case in which there is no solution in H0 1(¿).

Palabras clave del autor

    Palabras clave indexadas

      Detalles de financiación