PERIODIC SOLUTIONS FOR INDEFINITE SINGULAR EQUATIONS WITH SINGULARITIES IN THE SPATIAL VARIABLE AND NON-MONOTONE NONLINEARITY

TWe prove the existence of T-periodic solutions for the second order non-linear equation (u'/root 1-u'(2))' = h(t)g(u), where the non-linear term g has two singularities and the weight function h changes sign. We find a relation between the degeneracy of the zeroes of the weight function and the order of one of the singularities of the non-linear term. The proof is based on the classical Leray-Schauder continuation theorem. Some applications to important mathematical models are presented.