# zbMATH — the first resource for mathematics

##### Examples
 Geometry Search for the term Geometry in any field. Queries are case-independent. Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact. "Topological group" Phrases (multi-words) should be set in "straight quotation marks". au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted. Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff. "Quasi* map*" py: 1989 The resulting documents have publication year 1989. so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14. "Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic. dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles. py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses). la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

##### Operators
 a & b logic and a | b logic or !ab logic not abc* right wildcard "ab c" phrase (ab c) parentheses
##### Fields
 any anywhere an internal document identifier au author, editor ai internal author identifier ti title la language so source ab review, abstract py publication year rv reviewer cc MSC code ut uncontrolled term dt document type (j: journal article; b: book; a: book article)
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)].

##### MSC:
 34B10 Nonlocal and multipoint boundary value problems for ODE 34B15 Nonlinear boundary value problems for ODE 47H10 Fixed-point theorems for nonlinear operators on topological linear spaces 34B18 Positive solutions of nonlinear boundary value problems for ODE
Full Text:
##### References:
 [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)