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

Abstract

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 dim Ker L = 1 $\operatorname{dim}\operatorname{Ker}L = 1$ . And an example is given to show that our result here is valid.

Keywords

• Functional boundary conditions
• Mawhin’s continuation theorem
• Fredholm operator
• Resonance
• Half-line