# zbMATH — the first resource for mathematics

Positive solutions to a multi-point higher order boundary value problem. (English) Zbl 1101.34004
The authors study existence and nonexistence of positive solutions to the higher order multi-point boundary value problem
$u^{(n)}(t)+\lambda g(t)f(u(t))=0,$
$u(0)=u'(0)=\cdots =u^{(n-2)}(0)=0,\quad \sum^m_{i=1}a_i u^{(n-2)}(\xi_i)=u^{(n-2)}(1),$ with $$a_i>0, \;i=1, \cdots, m$$, $$\sum^m_{i=1}a_i=1$$, and $$\frac1 2\leq \xi_1<\cdots<\xi_m<1$$. For related results, see R. Ma and L. Ren [Appl. Math. Lett. 16, 863-869 (2003; Zbl 1070.34039)].
Reviewer: Ruyun Ma (Lanzhou)

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 47H10 Fixed-point theorems 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
Full Text:
##### References:
 [1] Agarwal, R.P., Focal boundary value problems for differential and difference equations, (1998), Kluwer Academic Dordrecht · Zbl 0914.34001 [2] Agarwal, R.P.; O’Regan, D.; Wong, P.J.Y., Positive solutions of differential, difference, and integral equations, (1998), Kluwer Academic Dordrecht · Zbl 0933.39025 [3] Cao, D.; Ma, R., Positive solutions to a second order multi-point boundary value problem, Electron. J. differential equations, 2000, 1-8, (2000) [4] Dulácska, E., Soil settlement effects on buildings, Developments in geotechnical engineering, vol. 69, (1992), Elsevier Amsterdam [5] Krasnosel’skii, M.A., Positive solutions of operator equations, (1964), Noordhoff Groningen · Zbl 0121.10604 [6] Liu, X.; Qiu, J.; Guo, Y., Three positive solutions for second-order m-point boundary value problems, Appl. math. comput., 156, 733-742, (2004) · Zbl 1069.34014 [7] Love, A.E.H., A treatise on the mathematical theory of elasticity, (1944), Dover New York · Zbl 0063.03651 [8] Ma, R.; Ren, L., Positive solutions for nonlinear m-point boundary value problems of Dirichlet type via fixed point index theory, Appl. math. lett., 16, 863-869, (2003) · Zbl 1070.34039 [9] Mansfield, E.H., The bending and stretching of plates, Internat. ser. monogr. aeronautics astronautics, vol. 6, (1964), Pergamon New York · Zbl 0125.42002 [10] Prescott, J., Applied elasticity, (1961), Dover New York · JFM 50.0554.12 [11] Soedel, W., Vibrations of shells and plates, (1993), Dekker New York · Zbl 0865.73002 [12] Timoshenko, S.P., Theory of elastic stability, (1961), McGraw-Hill New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.