Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales.
We establish the existence and uniqueness theorems for a linear and a nonlinear fourth-order boundary value problem. The results obtained generalize the results of Usmani [4] and Yang [5]. The methods used are based, in principle, on [3], [5].
We consider the existence of at least one positive solution to the dynamic boundary value problem where is an arbitrary time scale with and satisfying , , , , and where the boundary conditions at and can be both nonlinear and nonlocal. This extends some recent results on second-order semipositone dynamic boundary value problems, and we illustrate these extensions with some examples.
In the paper we prove an Ambrosetti-Prodi type result for solutions of the third-order nonlinear differential equation, satisfying .
Let be the Banach space of -functions on with the sup norm and be continuous increasing functionals, . This paper deals with the functional differential equation (1) , where is locally bounded continuous operator. Some theorems about the existence of two different solutions of (1) satisfying the functional boundary conditions , are given. The method of proof makes use of Schauder linearizatin technique and the Schauder fixed point theorem. The results are modified for 2nd order functional...