The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian
Liu, Bing ; Yu, Jianshe
Annales Polonici Mathematici, Tome 75 (2000), p. 271-280 / Harvested from The Polish Digital Mathematics Library
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We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: -(ϕp(x'))'+d/dtgradF(x)+g(t,x(t),x(δ(t)), x’(t), x’(τ(t))) = 0, t ∈ [0,1]; x(t)=φ̲(t), t ≤ 0; x(t)=φ¯(t), t ≥ 1. An existence result is obtained with the help of the Leray-Schauder degree theory, with no restriction on the damping forces d/dt grad F(x).

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:208400 
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Liu, Bing; Yu, Jianshe. The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian. Annales Polonici Mathematici, Tome 75 (2000) pp. 271-280. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv75z3p271bwm/

[000] [1] J. Lee and D. O'Regan, Existence results for differential delay equations I, J. Differential Equations 102 (1993), 342-359. | Zbl 0782.34070

[001] [2] J. Lee and D. O'Regan, Existence results for differential delay equations II, Nonlinear Anal. 17 (1991), 683-902.

[002] [3] B. Liu and J. S. Yu, Note on a third order boundary value problem for differential equations with deviating arguments, preprint. | Zbl 1026.34074

[003] [4] S. Ntouyas and P. Tsamatos, Existence and uniqueness for second order boundary value problems, Funkcial. Ekvac. 38 (1995), 59-69. | Zbl 0832.34015

[004] [5] S. Ntouyas and P. Tsamatos, Existence and uniquenes of solutions for boundary value problems for differential equations with deviating arguments, Nonlinear Anal. 22 (1994), 113-1-1146.

[005] [6] S. Ntouyas and P. Tsamatos, Existence of solutions of boundary value problems for differential equations with deviating arguments, via the topological transversality method, Proc. Roy. Soc. Edinburgh Sect. A 118 (1991), 79-89. | Zbl 0731.34076

[006] [7] M. R. Zhang, Nonuniform nonresonance at the first eigenvalue of the p-Laplacian, Nonlinear Anal. 29 (1997), 41-51. | Zbl 0876.35039