# 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 three positive pseudo-symmetric solutions for a one dimensional $p$-Laplacian. (English) Zbl 1028.34022
The five functionals fixed-point theorem due to {\it R. I. Avery} [Math. Sci. Res. Hot-Line 3, 9-14 (1999; Zbl 0965.47038)] is applied to obtain the existence of three positive pseudo-symmetric solutions to the three-point boundary value problem for a one-dimensional $p$-Laplacian $$(|u'|^{p-2}u')' + a(t)f(u) = 0, \quad u(0)=0,\ u(\theta) = u(1),$$ with $\theta \in (0,1)$.

##### MSC:
 34B18 Positive solutions of nonlinear boundary value problems for ODE
##### Keywords:
p-Laplacian; boundary value problems
Full Text:
##### References:
 [1] Agarwal, R. P.; O’regan, D.; Wong, P. J. Y.: Positive solutions of differential, difference and integral equations. (1999) [2] Avery, R. I.: Multiple positive solutions to boundary value problems, dissertation. (1997) [3] Avery, R. I.: A generalization of the Leggett--Williams fixed point theorem. MSR hot-line 2, 9-14 (1998) · Zbl 0965.47038 [4] Avery, R. I.; Henderson, J.: Three symmetric positive solutions for a second order boundary value problem. Appl. math. Lett. 13, 1-7 (2000) · Zbl 0961.34014 [5] Deimling, K.: Nonlinear functional analysis. (1985) · Zbl 0559.47040 [6] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones. (1988) · Zbl 0661.47045 [7] X.-M. He, W.-G. Ge, A remark on some three-point boundary value problems for the one-dimensional p-Laplacian, ZAMM, in press [8] Henderson, J.; Thompson, H. B.: Multiple symmetric positive solutions for a second order boundary value problem. Proc. amer. Math. soc. 128, 2373-2379 (2000) · Zbl 0949.34016 [9] Leggett, R. W.; Williams, L. R.: Multiple positive fixed points of nonlinear operators on ordered Banach spaces. Indiana univ. Math. J. 28, 673-688 (1979) · Zbl 0421.47033 [10] Zeidler, E.: Nonlinear functional analysis and its applications I: Fixed-point theorems. (1993) · Zbl 0794.47033