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Periodic solutions of dissipative dynamical systems with singular potential and p-Laplacian

100%

Liu B.

Annales Polonici Mathematici

2002

tom 79

nr 2

109-120

By using the topological degree theory and some analytic methods, we consider the periodic boundary value problem for the singular dissipative dynamical systems with p-Laplacian: $(ϕ_p(x'))' +d/dt gradF(x) + gradG(x) = e(t)$, x(0) = x(T), x'(0) = x'(T). Sufficient conditions to guarantee the existence of solutions are obtained under no restriction on the damping forces d/dt gradF(x).

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

63%

Liu B., Yu J.

Annales Polonici Mathematici

2000

tom 75

nr 3

271-280

We consider a boundary value problem for a differential equation with deviating arguments and p-Laplacian: $-(ϕ_{p}(x'))' + d/dt grad F(x) + g(t,x(t),x(δ(t))$, 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).

Ograniczanie wyników

2 Annales Polonici Mathematici

2 Liu B.

1 Yu J.

1 2002

1 2000

Wyniki wyszukiwania

Periodic solutions of dissipative dynamical systems with singular potential and p-Laplacian

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