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Topological degree methods for a Neumann problem governed by nonlinear elliptic equation


In this paper, we will use the topological degree, introduced by Berkovits, to prove existence of weak solutions to a Neumann boundary value problems for the following nonlinear elliptic equation

-diva(x,u,u)=b(x)|u|p-2u+λH(x,u,u),- div\,\,a\left( {x,u,\nabla u} \right) = b\left( x \right){\left| u \right|^{p - 2}}u + \lambda H\left( {x,u,\nabla u} \right),

where Ω is a bounded smooth domain of 𝕉N.