منابع مشابه
Nontrivial solutions for p-Laplacian systems
The paper deals with the existence and nonexistence of nontrivial nonnegative solutions for the sublinear quasilinear system div (|∇ui |p−2∇ui)+ λfi(u1, . . . , un)= 0 in Ω, ui = 0 on ∂Ω, i = 1, . . . , n, where p > 1, Ω is a bounded domain in RN (N 2) with smooth boundary, and fi , i = 1, . . . , n, are continuous, nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1 |ui |, we prove t...
متن کاملPositive radial solutions for p-Laplacian systems
The paper deals with the existence of positive radial solutions for the p-Laplacian system div(|∇ui| ∇ui) + f (u1, . . . , un) = 0, |x| < 1, ui(x) = 0, on |x| = 1, i = 1, . . . , n, p > 1, x ∈ R . Here f , i = 1, . . . , n, are continuous and nonnegative functions. Let u = (u1, . . . , un), ‖u‖ = ∑n i=1|ui|, f i 0 = lim‖u‖→0 f(u) ‖u‖p−1 , f i ∞ = lim‖u‖→∞ f(u) ‖u‖p−1 , i = 1, . . . , n, f = (f1...
متن کاملHIGHER INTEGRABILITY FOR PARABOLIC SYSTEMS OF p-LAPLACIAN TYPE
it is known that solutions locally belong to a slightly higher Sobolev space than assumed a priori. This self-improving property was first observed by Elcrat and Meyers in [ME] (see also [Gi] and [Str]). Their argument is based on reverse Hölder inequalities and a modification of Gehring’s lemma [Ge], which originally was developed to study the higher integrability of the Jacobian of a quasicon...
متن کاملCALDERÓN-ZYGMUND ESTIMATES FOR PARABOLIC p(x, t)-LAPLACIAN SYSTEMS
We prove local Calderón-Zygmund estimates for weak solutions of the evolutionary p(x, t)-Laplacian system ∂tu− div ( a(x, t)|Du|p(x,t)−2Du ) = div ( |F |p(x,t)−2F ) under the classical hypothesis of logarithmic continuity for the variable exponent p(x, t). More precisely, we show that the spatial gradient Du of the solution is as integrable as the right-hand side F , i.e. |F |p(·) ∈ Lqloc =⇒ |D...
متن کاملInverse nodal problem for p-Laplacian with two potential functions
In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2009
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2009.05.028