Solvability of second-order boundary-value problems at resonance involving integral conditions. (English) Zbl 1244.34020
Summary: This article concerns the second-order differential equation with integral boundary conditions
\[
\displaylines{ x''(t)=f(t,x(t),x'(t)),\quad t\in (0,1),\cr x(0)=\int_0^1x(s)d\alpha(s),\quad x(1)=\int_0^1x(s)d\beta(s). }
\]
Under resonance conditions, we construct a projector and then apply coincidence degree theory to establish the existence of solutions.
MSC:
34B10 | Nonlocal and multipoint boundary value problems for ordinary differential equations |
34B15 | Nonlinear boundary value problems for ordinary differential equations |
47N20 | Applications of operator theory to differential and integral equations |