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Journal of Analysis & Number Theory
An International Journal



The existence of positive solution for Choquard equations with Hardy-Littlewood-Sobolev critical exponents and Hardy-type term

S M Sbai,
Abstract :
We consider the following nonlinear Choquard equation with Dirichlet boundary condition. which involves the critical Sobolev exponent in the sense of the Hardy-Littlewood-Sobolev inequality and Hardy-type terms is considered. Under suitable assumptions on the function f and the parameter \mu>0, we are able to prove the existence of positive solutions. We achieve our goal by making use of variational methods. More specifically, the Mountain Pass Theorem.



G Thirupathi,
Abstract :
In this paper, we de fine a new subclass of analytic univalent function using q - differential operator, which generalizes Ruschewayh differential operators. Coefficient inequalities, Subordination, extreme points and integral means inequalities results are obtained.


Solutions for certain classes of Non-linear Diophantine Eqautions

Abstract :
ABSTRACT: The main aim of this paper is to introduce a method, to solve certain class of non-Linear Diophantine equations and investigate various properties using the well-known Eulerís theorem and the theory of congruence. Some of the interesting special cases of our main results have been discussed. KEY WORDS: Diophantine Equations, Non-linear Diophantine equations, Euler phi-function, Eulerís theorem.


Two Dimensional Laplace Transforms for Solving Systems of Fractional Partial Differential Equations

M.R. Masomi,
Abstract :
Abstract In this work, the authors implemented two dimensional Laplace transform to solve certain in homogenous sub ballistic fractional PDE and homogeneous systems of time fractional heat equations which is a generalization to the problem of thermal effects on fluid flow and also the problem of the effect of a uniform overburden on the passage of a thermal wave and the temperatures in the underlying rock. Constructive examples are also provided.

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