Existence and multiplicity of solutions for a class of elliptic systems in image Original Research Article

Using minimax methods we study the existence and multiplicity of nontrivial solutions for semilinear elliptic systems of the form View the MathML source−Δui+ai(x)ui=fi(x,u1,…,um)forx∈Rnandi=1,…,m. Turn MathJax on The potentials ai(x)ai(x) for i=1,…,mi=1,…,m may change sign, control the growth of nonlinearities and can be “large” at the infinity. We treat both superquadratic situation and nonquadratic situation at infinity on the nonlinearities fi(x,u1,…,um)fi(x,u1,…,um) for i=1,…,mi=1,…,m.