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We consider the perturbed nonlinear elliptic system -ε2Δu+V(x)u=K(x)|u|2*-2u+Hu(u,v),  x∈ℝN, -ε2Δv+V(x)v=K(x)|v|2*-2v+Hv(u,v),  x∈ℝN, where N≥3,2*=2N/(N-2) is the Sobolev critical exponent. Under proper conditions on V, H, and K, the existence result and multiplicity of the system are obtained by using variational method provided ε is small enough

abstract and applied analysis

Existence of Nontrivial Solutions for Perturbed Elliptic System in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:msup><mml:mrow><mml:mi>ℝ</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math>

Existence of Nontrivial Solutions for Perturbed Elliptic System inℝN