zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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 results for the problem $(\varphi(u'))'= f(t,u,u')$ with nonlinear boundary conditions. (English) Zbl 0920.34029
The authors prove an existence result for problems of the form $$(\phi(u'))'= f(t,u,u')\text{ a.e. }t\in [a,b],\ g(u(a), u'(a), u'(b))= 0,\ h(u(a))= u(b),$$ where $\phi$ is continuous and increasing from $\bbfR$ onto $\bbfR$. The main tools are the method of lower and upper solutions, the Nagumo condition and the Schauder fixed point theorem.

34B15Nonlinear boundary value problems for ODE
Full Text: DOI
[1] Cabada, A.; Pouso, R. L.: Existence result for the problem({$\phi$}(u’))’=$f(t,u,u')$ with periodic and Neumann boundary conditions. Nonlinear anal. T.M.A. 30, 1733-1742 (1997) · Zbl 0896.34016
[2] Decoster, C.: Pairs of positive solutions for the one-dimensionalp-Laplacian. Nonlinear anal. T.M.A. 23, 669-681 (1994)
[3] Fabry, Ch.; Habets, P.: Upper and lower solutions for second-order boundary value problems with nonlinear boundary conditions. Nonlinear anal. T.M.A. 10, 985-1007 (1986) · Zbl 0612.34015
[4] Lloyd, N. G.: Degree theory. (1978) · Zbl 0367.47001
[5] Mcshane, E. J.: Integration. (1967) · Zbl 0146.07202
[6] O’regan, D.: Some general principles and results for({$\phi$}(y’))’=$qf(t,y,y')$,0t1. SIAM J. Math. anal. 24, 648-668 (1993)
[7] O’regan, D.: Existence theory for({$\phi$}(y’))’=$qf(t,y,y')$,0t1. Commun. appl. Anal. 1, 33-52 (1997)
[8] Wang, M. X.; Cabada, A.; Nieto, J. J.: Monotone method for nonlinear second order periodic boundary value problems with Carathéodory functions. Ann. polon. Math. 58, 221-235 (1993) · Zbl 0789.34027
[9] Wang, J.; Gao, W.: Existence of solutions to boundary value problems for a nonlinear second order equation with weak Carathéodory functions. Differential equations and dyn. Systems 5, No. 2, 175-185 (1997) · Zbl 0891.34022
[10] Wang, J.; Gao, W.; Lin, Z.: Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem. T^ohoku math. J. 47, 327-344 (1995) · Zbl 0845.34038