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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 {\it R. Ma} and {\it L. Ren} [Appl. Math. Lett. 16, 863-869 (2003; Zbl 1070.34039)].

34B10Nonlocal and multipoint boundary value problems for ODE
34B15Nonlinear boundary value problems for ODE
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
34B18Positive solutions of nonlinear boundary value problems for ODE
Full Text: DOI
[1] Agarwal, R. P.: Focal boundary value problems for differential and difference equations. (1998) · Zbl 0914.34001
[2] Agarwal, R. P.; O’regan, D.; Wong, P. J. Y.: Positive solutions of differential, difference, and integral equations. (1998)
[3] Cao, D.; Ma, R.: Positive solutions to a second order multi-point boundary value problem. Electron. J. Differential equations 2000, 1-8 (2000) · Zbl 0964.34022
[4] Dulácska, E.: Soil settlement effects on buildings. Developments in geotechnical engineering 69 (1992)
[5] Krasnosel’skii, M. A.: Positive solutions of operator equations. (1964)
[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) · 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 6 (1964) · Zbl 0125.42002
[10] Prescott, J.: Applied elasticity. (1961) · Zbl 50.0554.12
[11] Soedel, W.: Vibrations of shells and plates. (1993) · Zbl 0865.73002
[12] Timoshenko, S. P.: Theory of elastic stability. (1961)