Multiplicidade de solucões nodais para um problema do tipo Yamabe

Abstract

In this work, we study the existence and multiplicity of solutions for the following class of Yamabe-type equations −divg(a(x)∇gu) + b(x)u = c(x)|u| 2 ∗−2u, where (M, g) is a compact Riemannian manifold without boundary of dimension m > 3, a, b, c ∈ C ∞(M), with a and c positive functions, and 2∗ = 2m m−2 denotes the critical Sobolev exponent. Assuming that the operator −divg(a∇g) + b is coercive and some hypotheses of symmetry on the manifold M, by applying the Concentration-Compactness Principle and a variational method for nodal solutions, we prove the existence of a positive solution and multiple nodal solutions.