## Existence of solutions to functional boundary value problem of second-order nonlinear differential equation.(English)Zbl 1208.34020

The paper deals with the existence of solutions of the second order differential equation
$x''(t)=f(t,x(t),x'(t)),\quad t\in(0,1),$
satisfying some conditions of the form $$\Gamma_1(x)=\Gamma_2(x)=0,$$ where $$\Gamma_1$$ and $$\Gamma_2$$ are continuous linear functionals. The authors impose appropriate conditions to guarantee the applicability of Mawhin’s coincidence degree theory in the nonresonance case, as well as when $$\dim\ker L=1$$ and $$\dim\ker L=2$$, where $$Lx:=x''$$.

### 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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### References:

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