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The existence of positive solution for Choquard equations with Hardy-Littlewood-Sobolev critical exponents and Hardy-type term
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S M Sbai,
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Abstract
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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. |
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CERTAIN SUBCLASS OF ANALYTIC UNIVALENT FUNCTIONS USING q DIFFERENTIAL OPERATOR
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G Thirupathi,
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Abstract
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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. |
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Solutions for certain classes of Non-linear Diophantine Eqautions
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ANTENEH TILAHUN,
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Abstract
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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 Euler’s 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, Euler’s theorem.
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Two Dimensional Laplace Transforms for Solving Systems of Fractional Partial Differential Equations
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M.R. Masomi,
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Abstract
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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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