A note on solvability of three-point boundary value problems for third-order differential equations with \(p\)-Laplacian. (English) Zbl 1151.34010

Liu, Xingyuan; Liu, Yuji

Tamkang J. Math. 39, No. 1, 95-103 (2008).

The authors study third-order three-point boundary value problems
\[ \begin{cases} [q(t)\phi(x''(t))]'+kx'(t)+g(t,x(t),x'(t))=p(t), & t \in(0,1), \\ x'(0)=x'(1)=x(\eta)=0. \end{cases} \]
By using topological degree theory, sufficient conditions for the existence of at least one solution of the above problem are established. The result obtained in this paper improves some existing results.

Reviewer: Minghe Pei (Jilin)

MSC:

34B10	Nonlocal and multipoint boundary value problems for ordinary differential equations
47N20	Applications of operator theory to differential and integral equations
34B15	Nonlinear boundary value problems for ordinary differential equations

Keywords:

solution; three-point boundary value problem; third order differential equation with \(p\)-Laplacian