On some non-linear boundary value problems for ordinary differential equations
This paper is concerned with existence and uniqueness of solutions of the three-point problem . The problem is at resonance, in the sense that the associated linear problem has non-trivial solutions. We use the method of lower and upper solutions.
We investigate the existence and stability of solutions for higher-order two-point boundary value problems in case the differential operator is not necessarily positive definite, i.e. with superlinear nonlinearities. We write an abstract realization of the Dirichlet problem and provide abstract existence and stability results which are further applied to concrete problems.