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 \(Lx:=x''\).


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
Full Text: DOI


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