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On a new critical point theorem and some applications to discrete equations

Galewski M., Galewska E.

Opuscula Mathematica

2014

Vol. 34, no. 4

725--732

Using the Fenchel-Young duality we derive a new critical point theorem. We illustrate our results with solvability for certain discrete BVP. Multiple solutions are also considered.

A retract principle on discrete time scales

Diblik J., Ruzickova M., Vaclavikova B.

Opuscula Mathematica

2006

Vol. 26, no. 3

445-455

In this paper we discuss asymptotic behavior of solutions of a class of scalar discrete equations on discrete real time scales. A powerful tool for the investigation of various qualitative problems in the theory of ordinary differential equations as well as delayed differential equations is the retraction method. The development of this method is discussed in the case of the equation mentioned above. Conditions for the existence of a solution with its graph remaining in a predefined set are formulated. Examples are given to illustrate the results obtained.