abstract:The Schauder fixed point theorem is an extension of the Brouwer fixed point theorem to topological vector spaces, which may be of infinite dimension. It asserts that if K is a convex subset of a topological vector space V and T is a continuous mapping of K into itself so that T(K) is contained in a compact subset of K, then T has a fixed point.
Solutions for a class ofthirdordernonlineardifferentialequations are studied by using the LeraySchauder fixedpointtheoremand the method ofLiapunovfunction.