×

zbMATH — the first resource for mathematics

Solvability of a three-point nonlinear boundary-value problem. (English) Zbl 1206.34033
Summary: Using the Leray Schauder nonlinear alternative, we prove the existence of a nontrivial solution for the three-point boundary-value problem
\[ u''+f(t,u)= 0,\quad 0<t<1 \]
\[ u(0)= \alpha u'(0),\quad u(1)=\beta u'(\eta ), \]
where \(\eta \in (0,1)\), \(\alpha ,\beta \in \mathbb{R}\), \(f\in C([0,1] \times\mathbb{R},\mathbb{R})\). Some examples are given to illustrate the results obtained.

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
PDF BibTeX XML Cite
Full Text: EMIS EuDML