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)
Discontinuous functional differential equations with delayed or advanced arguments. (English) Zbl 06068423
Summary: We provide new results on the existence of extremal solutions for discontinuous differential equations with a deviated argument which can be either delayed or advanced. The boundary condition is allowed to be discontinuous and to depend functionally on the unknown solution.
MSC:
34K10Boundary value problems for functional-differential equations
References:
[1]Chi, H.; Bell, J.; Hassard, B.: Numerical solution of a nonlinear advance-delay-differential equation from nerve conduction theory, J. math. Biol. 24, No. 5, 583-601 (1986) · Zbl 0597.92009 · doi:10.1007/BF00275686
[2]M.A. Domínguez-Pérez, R. Rodríguez-López, Multipoint boundary value problems of Neumann type for functional differential equations, Nonlinear Anal. Real World Applications, in press, doi:10.1016/j.nonrwa.2011.11.023.
[3]Dyki, A.: Boundary problems for differential equations with advanced arguments, Nonlinear stud. 15, No. 2, 123-135 (2008) · Zbl 1191.34083
[4]Franco, D.; Pouso, R. L.: Nonresonance conditions and extremal solutions for first-order impulsive problems under weak assumptions, Anziam j. 44, 393-407 (2003) · Zbl 1040.34009 · doi:10.1017/S1446181100008105
[5]Heikkilä, S.; Lakshmikantham, V.: Monotone iterative techniques for discontinuous nonlinear differential equations, (1994)
[6]Hutchinson, G. E.: Circular causal systems in ecology, Ann. New York acad. Sci. 50, 221-248 (1948)
[7]Ilea, V. A.; Serban, M. A.: An existence result of the solution for mixed type functional differential equations with parameter, Nonlinear anal. Forum 12, No. 1, 59-65 (2007) · Zbl 1156.34339
[8]Jankowski, T.: Advanced differential equations with nonlinear boundary conditions, J. math. Anal. appl. 304 (2005) · Zbl 1092.34032 · doi:10.1016/j.jmaa.2004.09.059
[9]Jankowski, T.: On delay differential equations with nonlinear boundary conditions, Bound. value. Probl. 2, 201-214 (2005) · Zbl 1148.34043 · doi:10.1155/BVP.2005.201
[10]Jankowski, T.: Existence of positive solutions to third order differential equations with advance arguments and nonlocal boundary value conditions, Nonlinear anal. 75, 913-923 (2012)
[11]Jiang, D.; Wei, J.: Monotone method for first- and second-order periodic boundary value problems and periodic solutions of functional differential equations, Nonlinear anal. 50, 885-898 (2002) · Zbl 1014.34049 · doi:10.1016/S0362-546X(01)00782-9
[12]Liz, E.; Nieto, J. J.: Periodic boundary value problems for a class of functional differential equations, J. math. Anal. appl. 200, 680-686 (1996) · Zbl 0855.34080 · doi:10.1006/jmaa.1996.0231
[13]May, R. M.: Stability and complexity in model ecosystems, (1975)
[14]A.J. Nicholson, The self-adjustment of populations to change, in: Cold Spring Harbor Symposia of Quantitative Biology, vol. 22, 1957, pp. 153 – 173.
[15]Nieto, J. J.; Rodríguez-López, R.: Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions, Comput. math. Appl. 40, 433-442 (2000) · Zbl 0958.34055 · doi:10.1016/S0898-1221(00)00171-1
[16]Nieto, J. J.; Rodríguez-López, R.: Remarks on periodic boundary value problems for functional differential equations, J. comput. Appl. math. 158, 339-353 (2003) · Zbl 1036.65058 · doi:10.1016/S0377-0427(03)00452-7
[17]Rustichini, A.: Functional-differential equations of mixed type: the linear autonomous case, J. dyn. Differ. equat. 1, No. 2, 121-143 (1989) · Zbl 0684.34065 · doi:10.1007/BF01047828
[18]Rustichini, A.: Hopf bifurcation for functional – differential equations of mixed type, J. dyn. Differ. equat. 1, No. 2, 145-177 (1989) · Zbl 0684.34070 · doi:10.1007/BF01047829
[19]Tamasan, A.: Extremal solutions for the discontinuous delay-equations, Studia univ. Babes-bolyai math. 41, No. 4, 107-112 (1996) · Zbl 1020.34057
[20]Yusufoglu, E.: An efficient algorithm for solving generalized pantograph equations with linear functional argument, Appl. math. Comput. 217, No. 7, 3591-3595 (2010) · Zbl 1204.65083 · doi:10.1016/j.amc.2010.09.005
[21]Webb, J. R. L.: Existence of positive solutions for a thermostat model, Nonlinear anal. RWA 13, 923-938 (2012)