The main results of this paper establish, via the variational method, the multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents under the presence of symmetry. The concentration-compactness principle allows to prove that the Palais-Smale condition is satisfied below a certain level.
In this article we use variational methods to study a strongly coupled elliptic system depending on a positive parameter λ. We suppose that the potentials are nonnegative and the intersection of the sets where they vanish has positive measure. A technical condition, imposed on the product of the potentials, allows us to consider a setting where we do not assume any positive lower bound for the potentials. Considering the associated functional, defined on an appropriated subspace of D 1,2 (R N ) × D 1,2 (R N ), we are able to establish results on the existence and multiplicity of solutions for the system when the parameter λ is sufficiently large.We also study the asymptotic behavior of these solutions when λ → ∞.
We study the existence of multiple solutions for a quasilinear elliptic system of gradient type with critical growth and the possibility of coupling on the subcritical term. The solutions are obtained from a version of the Symmetric Mountain Pass Theorem. The Concentration-Compactness Principle allows to verify that the Palais-Smale condition is satisfied below a certain level.2000 Mathematics Subject Classification: 35J60, 35J50, 35J55.
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