Paper's Title:

The Boundedness of Gradient Solutions of P-Laplacian Type

Author(s):

Corina Karim, Khoirunisa, Ratno Bagus Edy Wibowo

Department of Mathematics,
Universitas Brawijaya,
Veteran Street, Malang,
Indonesia.
E-mail: co_mathub@ub.ac.id
khrnisa@student.ub.ac.id
rbagus@ub.ac.id

Abstract:

In this paper, we give the boundedness of gradient solutions result for p-Laplacian systems only in the singular case. The Lebesgue space for initial data belong to guarantee the local boundedness of gradient solutions.

Paper's Title:

Local Boundedness of Weak Solutions for Singular Parabolic Systems of p-Laplacian Type

Author(s):

Corina Karim, Marjono

Department of Mathematics,
Universitas Brawijaya,
Indonesia.
E-mail:  co_mathub@ub.ac.id, marjono@ub.ac.id

Abstract:

We study the local boundedness of weak solutions for evolutional p-Laplacian systems in the singular case. The initial data is belonging to Lebesgue space L^∞ (0,T;W^(1,p) (Ω,Rⁿ )). We use intrinsic scaling method to treat the boundedness of weak solutions. The main result is to make the local boundedness of weak solution for the systems well-worked in the intrinsic scaling.

Paper's Title:

Existence Results for Second Order Impulsive Functional Differential Equations with Infinite Delay

Author(s):

M. Lakrib, A. Oumansour and K. Yadi  

Laboratoire de Mathématiques, Université Djillali
Liabées, B.P. 89 Sidi Bel Abbès 22000, Algérie
mlakrib@univ-sba.dz
oumansour@univ-sba.dz

Laboratoire de Mathématiques, Université Abou Bekr
Belkaid, B.P. 119 Tlemcen 13000, Algérie
k_yadi@mail.univ-tlemcen.dz

Abstract:

In this paper we study the existence of solutions for second order impulsive functional differential equations with infinite delay. To obtain our results, we apply fixed point methods.

Paper's Title:

Uniform Continuity and k-Convexity

Author(s):

Adel Afif Abdelkarim

Mathematics Department, Faculty of Science, J
erash University, Jerash
Jordan.

adelafifo_afifo@yahoo.com

Abstract:

A closed arcwise-connected subset A of Rⁿ is called k-convex if for each positive number a and for all elements x and y in A there is a positive number b such that if the norm of x-y is less than or equal to b then the length of the shortest curve l(x,y) in A is less than k times the norm of x-y plus a. We show that a union of two non disjoint closed finite convex subsets need not be k-convex. Let f(x) be a uniformly continuous functions on a finite number of closed subsets A_{1},...,A_{n} of R^{n} such that the union of A_{j},...,A_{n},j=1,...,n-1 is k-convex. We show that f is uniformly continuous on the union of the sets A_{i},i=1,...,n. We give counter examples if this condition is not satisfied. As a corollary we show that if f(x) is uniformly continuous on each of two closed convex sets A,B then f(x) is uniformly continuous on the union of A and B.

Paper's Title:

Some Properties of Cosine Series with Coefficients from Class of General Monotone Sequences Order r

Author(s):

Corina Karim, Moch. Aruman Imron

Department of Mathematics,
Universitas Brawijaya,
Indonesia.
E-mail: co_mathub@ub.ac.id
maimr@ub.ac.id

Abstract:

The coefficient of sine series from general monotone class has been generalized by Bogdan Szal to the new class which is called class of general monotone order r. This coefficient class is more general than class of general monotone introduced by Tikhonov. By special case, we study properties of cosine series with coefficient of sine series from the class of general monotone order r.

Paper's Title:

On a Problem on Periodic Functions

Author(s):

Adel A. Abdelkarim

Mathematics Department, Faculty of Science,
Jerash Private University, Jerash,
Jordan.

E-mail: adelafifo_afifo@yahoo.com
 

Abstract:

Given a continuous periodic real function f with n translates  f₁ ,..., f_n , where f_i(x)=f(x+a_i), i=1,...,n. We solve a problem by Erdos and Chang and show that there are rational numbers r,s such that f(r)≥ f_i(r), f(s)≤ f_i(s), i=1,...,n. No restrictions on the constants or any further restriction on the function f are necessary as was imposed earlier.

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