Boris Rudolf (1995)
Archivum Mathematicum
Similarity:
In the paper it is proved that each generalized boundary value problem for the n-th order linear differential equation generates a Fredholm mapping of index zero.
Bravyi, E. (2000)
Memoirs on Differential Equations and Mathematical Physics
Similarity:
Alaa Almansour, Paul Eloe (2015)
Annales Polonici Mathematici
Similarity:
We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a...
Jolanta Przybycin (1997)
Annales Polonici Mathematici
Similarity:
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].
Valter Šeda (1983)
Annales Polonici Mathematici
Similarity:
Vladimír Ďurikovič, Monika Ďurikovičová (2002)
Archivum Mathematicum
Similarity:
We are dealing with Dirichlet, Neumann and Newton type initial-boundary value problems for a general second order nonlinear evolution equation. Using the Fredholm operator theory we establish some sufficient conditions for Fréchet differentiability of associated operators to the given problems. With help of these results the generic properties, existence and continuous dependency of solutions for initial-boundary value problems are studied.