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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
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