Multiple solutions for systems of differential equations with nonlinear boundary conditions - Jutarat Kongson (2018)
We establish the existence of three solutions in admissible bounding sets for systems of nonlinear differential equations of the form y'' = f (x;y;y'), x Ie ∈ [0;1] satisfying the fully nonlinear boundary conditions g((y(0);y(1)); (y'(0);y'(1))) = 0: We assume that f and g are continuous, that g is compatible with the admissible bounding sets, and that f satisfies a Nagumo-type condition that guarantees a priori bounds on the derivatives of solutions. We use Leray-Schauder degree theory in novel spaces. © CSP - Cambridge, UK; I & S - Florida, USA, 2011.