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Discontinuous functional differential equations with delayed or advanced arguments. (English) Zbl 1323.34080
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.
34K10Boundary value problems for functional-differential equations
Full Text: DOI
[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) · Zbl 0804.34001
[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) · Zbl 1235.34179
[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) · Zbl 1238.34033