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)
Third-order boundary value problems with sign-changing solutions. (English) Zbl 1130.34010
The authors are concerned with the existence of sign-changing solutions for a third order differential equation $$u'''(t)=f(t,u(t),u'(t),u''(t)),\quad\text{ a.e. } t\in (0,1),$$ subject to the boundary conditions $u(0)=u'(0)=u''(1)=0$ or $u(0)=u'(1)=u''(1)=0$. The proof of the main results are based on the Leray-Schauder continuation principle.

MSC:
34B15Nonlinear boundary value problems for ODE
WorldCat.org
Full Text: DOI
References:
[1] Anderson, D. R.: Green’s function for a third-order generalized right focal problem. J. math. Anal. appl. 288, No. 1, 1-14 (2003) · Zbl 1045.34008
[2] Chu, J.; Zhou, Z.: Positive solutions for singular non-linear third-order periodic boundary value problems. Nonlinear anal. 64, No. 11, 1528-1542 (2006) · Zbl 1099.34025
[3] García-Huidobro, M.; Gupta, C. P.; Manásevich, R.: A Dirichlet--Neumann m-point BVP with a p-Laplacian-like operator. Nonlinear anal. 62, No. 6, 1067-1089 (2005) · Zbl 1082.34011
[4] Graef, J. R.; Yang, B.: Positive solutions of a nonlinear third order eigenvalue problem. Dynam. systems appl. 15, 97-110 (2006) · Zbl 1106.34013
[5] Gupta, C. P.: A new a priori estimate for multi-point boundary-value problems. Electron. J. Differ. equ. Conf. 7, 47-59 (2001) · Zbl 0980.34009
[6] Gupta, C. P.: A priori estimates and solvability of a generalized multi-point boundary value problem. Dynam. systems appl. 3, 249-256 (2001) · Zbl 1012.34013
[7] Gupta, C. P.: A non-resonant multi-point boundary value problem of Neumann--Dirichlet type for a p-Laplacian type operator. Dynam. systems appl. 4, 439-442 (2004) · Zbl 1069.34013
[8] Gupta, C. P.; Lakshmikantham, V.: Existence and uniqueness theorems for a third-order three-point boundary value problem. Nonlinear anal. 16, No. 11, 949-957 (1991) · Zbl 0826.34017
[9] Gupta, C. P.; Trofimchuk, S.: A priori estimates for the existence of a solution for a multi-point boundary value problem. J. inequal. Appl. 5, No. 4, 351-365 (2000) · Zbl 0967.34006
[10] Henderson, J.; Yin, W. K. C.: Existence of solutions for third-order boundary value problems on a time scale. Comput. math. Appl. 45, 1101-1111 (2003) · Zbl 1057.39011
[11] Jiang, D.; Agarwal, R. P.: A uniqueness and existence theorem for a singular third-order boundary value problem on [0,\infty). Appl. math. Lett. 15, No. 4, 445-451 (2002) · Zbl 1021.34020
[12] Ma, R.: Multiplicity results for a third order boundary value problem at resonance. Nonlinear anal. 32, No. 4, 493-499 (1998) · Zbl 0932.34014
[13] O’regan, D.; Precup, R.: Theorems of Leray--Schauder type and applications. Series in mathematical analysis and applications 3 (2001)
[14] Sun, Y.: Positive solutions of singular third-order three-point boundary value problem. J. math. Anal. appl. 306, No. 2, 589-603 (2005) · Zbl 1074.34028
[15] Wong, P. J. Y.: Constant-sign solutions for a system of third-order generalized right focal problems. Nonlinear anal. 63, e2153-e2163 (2005)
[16] Zeidler, E.: Nonlinear functional analysis and applications, I: Fixed point theorems. (1986) · Zbl 0583.47050