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A fixed-point approach for decaying solutions of difference equations: A fixed point approach to discrete BVPs

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Rok publikování 2021
Druh Článek v odborném periodiku
Časopis / Zdroj Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Fakulta / Pracoviště MU

Přírodovědecká fakulta

Klíčová slova boundary value problem on the half line; decaying solution; fixed-point theorem; functional discrete equations; nonlinear difference equation
Popis A boundary value problem associated with the difference equation with advanced argument * Delta(an phi(Delta xn))+bn phi(xn+p)=0,n >= 1 is presented, where phi(u) = |u|(alpha)sgn u, alpha > 0, p is a positive integer and the sequences a, b, are positive. We deal with a particular type of decaying solution of (*), that is the so-called intermediate solution (see below for the definition). In particular, we prove the existence of this type of solution for (*) by reducing it to a suitable boundary value problem associated with a difference equation without deviating argument. Our approach is based on a fixed-point result for difference equations, which originates from existing ones stated in the continuous case. Some examples and suggestions for future research complete the paper. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.
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