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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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