In this paper, we study the existence of multiple solutions for operator equations involving homogeneous potential operators. With the help of the Nehari manifold and the fibering method, we prove that some such equations have at least two nonzero solutions. Furthermore, we apply this result to prove the existence of two positive solutions for some quasilinear elliptic problems involving sign-changing weight functions.
"A fibering map approach to a potential operator equation and its applications." Differential Integral Equations 22 (11/12) 1097 - 1114, November/December 2009. https://doi.org/10.57262/die/1356019406