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On four-point boundary value problem without growth conditions

Irena Rachůnková (1999)

Czechoslovak Mathematical Journal

We prove the existence of solutions of four-point boundary value problems under the assumption that f fulfils various combinations of sign conditions and no growth restrictions are imposed on f . In contrast to earlier works all our results are proved for the Carathéodory case.

On four-point boundary value problems for differential inclusions and differential equations with and without multivalued moving constraints

Adel Mahmoud Gomaa (2012)

Czechoslovak Mathematical Journal

We deal with the problems of four boundary points conditions for both differential inclusions and differential equations with and without moving constraints. Using a very recent result we prove existence of generalized solutions for some differential inclusions and some differential equations with moving constraints. The results obtained improve the recent results obtained by Papageorgiou and Ibrahim-Gomaa. Also by means of a rather different approach based on an existence theorem due to O. N. Ricceri...

On some three-point problems for third-order differential equations

Irena Rachůnková (1992)

Mathematica Bohemica

This paper is concerned with existence and uniqueness of solutions of the three-point problem u ' ' ' = f ( t , u , u ' , u ' ' ) , u ( c ) = 0 , u ' ( a ) = u ' ( b ) . u ' ' ( a ) = u ' ' ( b ) , a c b . 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.

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