Existence of solutions for functional boundary value problems at resonance on the half-line

Abstract

By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

Solvability of mixed Hilfer fractional functional boundary value problems with p-Laplacian at resonance

“…In recent years, some scholars have changed the boundary value conditions into abstract conditions, which contains many specific boundary conditions. And many achievements have been made in the study of functional boundary value problems [12][13][14][15][16][17].…”

On the Existence of Coupled Fractional Jerk Equations with Multi-Point Boundary Conditions

“…During the last two decades, great interest has been devoted to the study of fractional differential equations, which can serve as an excellent tool for the mathematical modeling of systems and processes in the fields of physics, chemistry, biology, electromagnetic, mechanics, economics, dynamical processes, etc. For more details regarding fractional differential equations involving initial or boundary conditions, see for instance, [21][22][23][24][25][26][27][28][29][30][31] and the references therein.…”