Two Types of Solutions to a Class of -Laplacian Systems with Critical Sobolev Exponents in

We focus on the following elliptic system with critical Sobolev exponents:  ; ; , where , either or , and critical Sobolev exponents and . Conditions on potential functions lead to no compact embedding. Relying on concentration-compactness principle, mountain pass lemma, and genus theory, the existence of solutions to the elliptic system with or will be established.

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