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

Bing LiuJianshe Yu — 2000

Annales Polonici Mathematici

We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: - ( ϕ p ( x ' ) ) ' + d / d t g r a d F ( x ) + g ( t , x ( t ) , x ( δ ( t ) ) , x’(t), x’(τ(t))) = 0, t ∈ [0,1]; x ( t ) = φ ̲ ( 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).

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