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Your search keyword '"Georgiev Georgiev, Svetlin"' showing total 4 results
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4 results on '"Georgiev Georgiev, Svetlin"'

1. On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs

Author

Georgiev Georgiev, Svetlin and Mebarki, Karima

Subjects
Class (set theory), Pure mathematics, Sum of operators, Differential equation, odes, law.invention, Positive solution, law, QA1-939, Fixed point index, ODEs, Mathematics, QA299.6-433, Partial differential equation, Ode, Fixed-point index, sum of operators, Lipschitz continuity, cone, pdes, Invertible matrix, positive solution, Ordinary differential equation, Geometry and Topology, PDEs, fixed point index, Cone, Analysis
Abstract

[EN] The aim of this work is two fold: first we extend some results concerning the computation of the fixed point index for the sum of an expansive mapping and a $k$-set contraction obtained in \cite{DjebaMeb, Svet-Meb}, to the case of the sum $T+F$, where $T$ is a mapping such that $(I-T)$ is Lipschitz invertible and $F$ is a $k$-set contraction. Secondly, as illustration of some our theoretical results, we study the existence of positive solutions for two classes of differential equations, covering a class of first-order ordinary differential equations (ODEs for short) posed on the positive half-line as well as a class of partial differential equations (PDEs for short)., Direction Générale de la Recherche Scientifique et du Développement Technologique DGRSDT. MESRS Algeria. Projet PRFU: C00L03UN060120180009

Published
2021

2. On fixed point index theory for the sum of operators and applications to a class of ODEs and PDEs

Author

Direction Générale de la Recherche Scientifique et du Développement Technologique, Argelia, Georgiev Georgiev, Svetlin, Mebarki, Karima, Direction Générale de la Recherche Scientifique et du Développement Technologique, Argelia, Georgiev Georgiev, Svetlin, and Mebarki, Karima

Abstract

[EN] The aim of this work is two fold: first we extend some results concerning the computation of the fixed point index for the sum of an expansive mapping and a $k$-set contraction obtained in \cite{DjebaMeb, Svet-Meb}, to the case of the sum $T+F$, where $T$ is a mapping such that $(I-T)$ is Lipschitz invertible and $F$ is a $k$-set contraction. Secondly, as illustration of some our theoretical results, we study the existence of positive solutions for two classes of differential equations, covering a class of first-order ordinary differential equations (ODEs for short) posed on the positive half-line as well as a class of partial differential equations (PDEs for short).

Published
2021

3. Bi-α ISO-DIFFERENTIAL INEQUALITIES AND APPLICATIONS.

Author

Georgiev Georgiev, Svetlin

Subjects
DIFFERENTIAL equations, MULTIPLICATION, DIFFERENTIAL inequalities, MATHEMATICAL inequalities, UNIQUENESS (Mathematics)
Abstract

In this lecture, firstly we deduct some multiplicative iso-differential inequalities for multiplicative iso-functions of first, second, third, fourth and fifth kind. Then they are deducted and proved some bi-α-multiplicative iso-differential inequalities. As applications, in the lecture are deducted some uniqueness results for some classes multiplicative iso-differential equations and bi-α-multiplicative iso-differential equations. [ABSTRACT FROM AUTHOR]

Published
2019
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4. UNIFORM CONTINUITY OF THE SOLUTION MAP FOR NONLINEAR WAVE EQUATION IN REISSNER-NORDSTRÖM METRIC.

Author

Georgiev Georgiev, Svetlin

Subjects
*NUMERICAL solutions to the Cauchy problem, *CONTINUITY, *NONLINEAR wave equations, *MATHEMATICAL constants, *PARTIAL differential equations
Abstract

In this paper we study the properties of the solutions to the Cauchy problem (1) (utt - Δu)gs = f(u) + g(¦x¦), t ∈ [0, 1], x ∈ R³, (2) u(1, x) = u0 ∈ Ḣ¹(R³), ut(1, x) = u1 ∈ L²(R³), where gs is the Reissner-Nordström metric (see [2]); f ∈ C¹(R¹), f(0) = 0, a¦u¦ ≤ f' ≤ b¦u¦, g ∈ C(R+), g(¦x¦) ≥ 0, g(¦x¦) = 0 for ¦x¦ ≥ r1, a and b are positive constants, r1 > 0 is suitable chosen. When g(r) ≡ 0 we prove that the Cauchy problem (1), (2) has a nontrivial solution u(t, r) in the form u(t, r) = v(t)ω(r) ∈ C((0, 1] Ḣ¹(R+)), where r = ¦x¦, and the solution map is not uniformly continuous. When g(r) ≠ 0 we prove that the Cauchy problem (1), (2) has a nontrivial solution u(t, r) in the form u(t, r) = v(t)ω(r) ∈ C((0, 1] Ḣ¹(R+)), where r = ¦x¦, and the solution map is not uniformly continuous. [ABSTRACT FROM AUTHOR]

Published
2007
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