Multiplicative solutions for nonlinear delta fractional difference problems with parameter-dependent summation constraints

Le résumé fourni par la source

This paper studies a nonlinear class of fractional difference problems depending on parameter-dependent summation constraints. An explicit formula for the Green's function and its positivity and bounds for a specific interval of parameters are found. By use of the Guo–Krasnoselskii fixed point theorem with an appropriate cone, we obtain the existence criteria for multiple distinct positive solutions. This is achieved through a ‘trapping mechanism’ based on a series of alternating growth conditions of the nonlinearity. In addition, the use of the obtained results is justified through an illustrative example.

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