Three Solutions To A Class Of P(x)-Laplace Equation Based On Nehari Skill

This thesis shows the existence of at least three nontrivial solutions to the quasiliuear elliptic equation with Neumann boundary conditionor Dirichlet boundarv conditionin a smooth bounded domainΩ(?) Rⁿ. In addition, the thesis has proved that one solution is positive, one is negative, and the last one is of sign-changing propoty. The method used here is based on Nehari skills on three sub-manifolds of the spaceW^1,(p(x))(Ω) or W₀^1,(p(x))(Ω).