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

Annales Polonici Mathematici (2000)

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

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topLiu, 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

top- [1] J. Lee and D. O'Regan, Existence results for differential delay equations I, J. Differential Equations 102 (1993), 342-359. Zbl0782.34070
- [2] J. Lee and D. O'Regan, Existence results for differential delay equations II, Nonlinear Anal. 17 (1991), 683-902.
- [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] S. Ntouyas and P. Tsamatos, Existence and uniqueness for second order boundary value problems, Funkcial. Ekvac. 38 (1995), 59-69. Zbl0832.34015
- [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] 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] 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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