Abstract
Using minimax methods we study the existence and multiplicity of nontrivial solutions for semilinear elliptic systems of the form − Δ u i + a i ( x ) u i = f i ( x , u 1 , … , u m ) for x ∈ R n and i = 1 , … , m . The potentials a i ( x ) for i = 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 f i ( x , u 1 , … , u m ) for i = 1 , … , m .
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