Xian Wu

Existence and multiplicity of nontrivial solutions for a class of modified nonlinear fourth-order elliptic equations on R N

In this paper, we study the following fourth-order elliptic equation of the form ? 2 u - ? u + V ( x ) u - ? 2 ? ( u 2 ) u = h ( x , u ) , x ? R N , where ? 2 ? ? ( ? ) is the biharmonic operator, ? ? 0 , N ≤ 6 , V ? C ( R N , R ) and h ? C ( R N × R , R ) . Under appropriate assumptions on V ( x ) and h ( x , u ) , some existence and multiplicity results for nontrivial solutions are obtained via variational methods.

On equilibrium problem of abstract economy, generalized quasi-variational inequality, and an optimization problem in locally H-convex spaces

In this paper, the equilibrium existence problem for abstract economies, the existence problem for solution of generalized quasi-variational inequality, and an optimization problem in locally H-convex spaces are researched.