Potential conditions for solvability of semilinear boundary value problems

In this dissertation we apply a min-max principle, called the Saddle Point Theorem, to find solutions, in a generalized sense of boundary value problems for ordinary and partial differential equations. These conditions depend on the nonlinearity and its primitive (or antiderivative). We also establish a result related to the so called Ambrosseti-Prodi-Kasdan-Warner phenomenon (A.P.K.W.) by showing that, for large values of a parameter appearing in the equation, there are at least two solutions.The major part of the thesis is verifying that an abstract condition formulated by Palais and Smale is satisfied for functionals arising from the boundary value problems