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Existence of Solutions for a Class of p(x)-Kirchhoff Type Equation with Dependence on the Gradient

  • Lapa, Eugenio Cabanillas (Instituto de Investigacion, Facultad de Ciencias Matematicas-UNMSM) ;
  • Barros, Juan Benito Bernui (Instituto de Investigacion, Facultad de Ciencias Matematicas-UNMSM) ;
  • de la Cruz Marcacuzco, Rocio Julieta (Instituto de Investigacion, Facultad de Ciencias Matematicas-UNMSM) ;
  • Segura, Zacarias Huaringa (Instituto de Investigacion, Facultad de Ciencias Matematicas-UNMSM)
  • Received : 2017.05.29
  • Accepted : 2018.07.18
  • Published : 2018.09.23

Abstract

The object of this work is to study the existence of solutions for a class of p(x)-Kirchhoff type problem under no-flux boundary conditions with dependence on the gradient. We establish our results by using the degree theory for operators of ($S_+$) type in the framework of variable exponent Sobolev spaces.

Keywords

p(x)-Kirchhoff type equation;variable exponent Sobolev space;degree theory;gradient term

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