# 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)
Existence of positive solutions for a second-order ordinary differential system. (English) Zbl 1088.34016
This paper deals with the existence of positive solutions for the following system $$-u''(t)= f_1(t, u(t))+ h_1(u(t), v(t)),$$ $$-v''(t)= f_2(t, v(t))+ h_2(u(t), v(t)),\quad 0< t< 1,$$ $$u(0)= u(1)= v(0)= v(1)= 0,$$ where $f_1$ and $h_1$ are superlinear and $f_2$ and $h_2$ are sublinear. A concrete example is presented.

##### MSC:
 34B18 Positive solutions of nonlinear boundary value problems for ODE
Full Text:
##### References:
 [1] Ma, R.: Existence of positive radial solutions for elliptic systems. J. math. Anal. appl. 201, 375-386 (1996) · Zbl 0859.35040 [2] Dunninger, D. R.; Wang, H.: Existence and multiplicity of positive solutions for elliptic systems. Nonlinear anal. 29, 1051-1060 (1997) · Zbl 0885.35028 [3] Dunninger, D. R.; Wang, H.: Multiplicity of positive radial solutions for an elliptic system on an annulus. Nonlinear anal. 42, 803-811 (2000) · Zbl 0959.35051 [4] Lee, Y. H.: Multiplicity of positive radial solutions for multiparameter semilinear elliptic systems on an annulus. J. differential equations 174, 420-441 (2001) · Zbl 1001.34011 [5] Zhao, P.; Zhou, W.; Zhong, C.: The existence of three nontrival solutions of a class of elliptic systems. Nonlinear anal. 49, 431-443 (2002) · Zbl 1030.35047 [6] Zhong, C.; Fan, X.; Chen, W.: Introduction to nonlinear functional analysis. (1998) [7] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones. (1988) · Zbl 0661.47045