# The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian

• Volume: 75, Issue: 3, page 271-280
• ISSN: 0066-2216

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## Abstract

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We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-{\left({\varphi }_{p}\left({x}^{\text{'}}\right)\right)}^{\text{'}}+d/dtgradF\left(x\right)+g\left(t,x\left(t\right),x\left(\delta \left(t\right)\right)$, x’(t), x’(τ(t))) = 0, t ∈ [0,1]; $x\left(t\right)=\underline{\phi }\left(t\right),$ t ≤ 0; $x\left(t\right)=\overline{\phi }\left(t\right)$, 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).

## How to cite

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Liu, Bing, and Yu, Jianshe. "The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian." Annales Polonici Mathematici 75.3 (2000): 271-280. <http://eudml.org/doc/208400>.

@article{Liu2000,
abstract = {We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_\{p\}(x^\{\prime \}))^\{\prime \} + d/dt grad F(x) + g(t,x(t),x(δ(t))$, x’(t), x’(τ(t))) = 0, t ∈ [0,1]; $x(t)=\underline\{φ\}(t),$ t ≤ 0; $x(t) = \overline\{φ\}(t)$, 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).},
author = {Liu, Bing, Yu, Jianshe},
journal = {Annales Polonici Mathematici},
keywords = {a priori bounds; boundary value problems; existence theorems; differential equations with deviating arguments; Leray-Schauder degree; p-Laplacian; -Laplacian},
language = {eng},
number = {3},
pages = {271-280},
title = {The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian},
url = {http://eudml.org/doc/208400},
volume = {75},
year = {2000},
}

TY - JOUR
AU - Liu, Bing
AU - Yu, Jianshe
TI - The existence of solution for boundary value problems for differential equations with deviating arguments and p-Laplacian
JO - Annales Polonici Mathematici
PY - 2000
VL - 75
IS - 3
SP - 271
EP - 280
AB - We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_{p}(x^{\prime }))^{\prime } + d/dt grad F(x) + g(t,x(t),x(δ(t))$, x’(t), x’(τ(t))) = 0, t ∈ [0,1]; $x(t)=\underline{φ}(t),$ t ≤ 0; $x(t) = \overline{φ}(t)$, 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).
LA - eng
KW - a priori bounds; boundary value problems; existence theorems; differential equations with deviating arguments; Leray-Schauder degree; p-Laplacian; -Laplacian
UR - http://eudml.org/doc/208400
ER -

## References

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2. [2] J. Lee and D. O'Regan, Existence results for differential delay equations II, Nonlinear Anal. 17 (1991), 683-902.
3. [3] B. Liu and J. S. Yu, Note on a third order boundary value problem for differential equations with deviating arguments, preprint. Zbl1026.34074
4. [4] S. Ntouyas and P. Tsamatos, Existence and uniqueness for second order boundary value problems, Funkcial. Ekvac. 38 (1995), 59-69. Zbl0832.34015
5. [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.
6. [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. Zbl0731.34076
7. [7] M. R. Zhang, Nonuniform nonresonance at the first eigenvalue of the p-Laplacian, Nonlinear Anal. 29 (1997), 41-51. Zbl0876.35039

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