Periodic solutions of p-Laplacian systems with a nonlinear convection term
نویسندگان
چکیده
منابع مشابه
Periodic Solutions of p-Laplacian Systems with a Nonlinear Convection Term
((u1(x, t+ ω), (u2(x, t+ ω)) = (u1(x, t), u2(x, t)) in Q, where △pu = div(|∇u| p−2 ∇u) is the so-called p−Laplacian operator, Ω is a bounded convex subset in R , Q := Ω × (0, ω), S := ∂Ω × (0, ω), ∂Ω is the boundary of Ω and ω > 0. Precise conditions on ai, fi and hi will be given later. The system of form (S) is a class of degenerate parabolic systems and appears in the theory of non-Newtonian...
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where Ω RN (N 1) is a bounded domain with smooth boundary ∂Ω, ω > 0, m > 1, and b(u) is a nonlinear vector field such that b(u) k u β, with some k > 0, 0 β m 1. f (t) and h(x, t) are ω-periodic (in t) functions. Equation (1.1) is a class of degenerate parabolic equations and appears to be relevant in the theory of non-Newtonian fluids perturbed by nonlinear terms and forced by rather irregular ...
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In this paper, by using the least action principle in critical point theory, we obtain some existence theorems of periodic solutions for p(t)-Laplacian system d dt (|u̇(t)|p(t)−2u̇(t)) = ∇F (t, u(t)) a.e. t ∈ [0, T ] u(0)− u(T ) = u̇(0)− u̇(T ) = 0, which generalize some existence theorems. 2010 Mathematics Subject Classification: 34C25, 35A15
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The existence of periodic solutions of a higher order nonlinear functional difference equation with p-Laplacian is studied. Sufficient conditions for the existence of periodic solutions of such equation are established. The result is based on Mawhin′s continuation theorem. The methods used to estimate the priori bound on periodic solutions are very technical.
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ژورنال
عنوان ژورنال: Electronic Journal of Qualitative Theory of Differential Equations
سال: 2009
ISSN: 1417-3875
DOI: 10.14232/ejqtde.2009.1.68