The Solutions For A Fully Nonlinear Elliptic Equation With Neumann Boundary Problem

In this thesis,we prove the existence and multiplicity of solutions to the following fully nonlinear elliptic equation(?) Where Ω (?)RN RN is a bounded region with Lipschitz boundaries,N≥2;v represents the unit outer normal vector at point x∈ (?)Ω,and both f:Ω × R→R and g:(?)Ω×R→R are Caratheodory functions.The existence of solutions without Ambrosetti-Rabinowitz condition is obtained by the Mountain Pass theorem and the Fountain theorem.And the multiplicity results are obtained by the Symmetric Mountain Pass theorem and the Dual Fountain theorem.Finally,the existence of infinitely many solutions via Clark’s theorem is established.Since the problem is of strong nonlinearity,the working functional space is the Musielak-Orlicz-Sobolev space.