scholarly journals On Some Properties of Solutions of Polyharmonic Equation in Polyhedral Angles

2007 ◽  
Vol 14 (3) ◽  
pp. 565-580
Author(s):  
Ilia Tavkhelidze
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Fundamental Solutions ◽  
Asymptotic Behavior Of Solutions ◽  
Uniqueness Theorems ◽  
Energy Integral ◽  
Polyharmonic Operator ◽  
Polyharmonic Equation

Abstract For a higher order differential equation with the polyharmonic operator, the Dirichlet and Riquier boundary value problems are studied in some polyhedral angles. Uniqueness theorems for solutions with a bounded “energy integral” of the corresponding BVPs are proved. Recurrent formulas are constructed for representation of fundamental solutions and Green's functions. The asymptotic behavior of solutions at infinity is studied.

scholarly journals Mixed Boundary Value Problems for the Elasticity System in Exterior Domains

2019 ◽  
Vol 24 (2) ◽  
pp. 58
Author(s):  
Hovik A. Matevossian
Keyword(s):  
Asymptotic Behavior ◽  
Variational Principle ◽  
Mixed Boundary ◽  
Asymptotic Behavior Of Solutions ◽  
Compact Set ◽  
Uniqueness Theorems ◽  
Energy Integral ◽  
Exterior Domains ◽  
Mixed Problems ◽  
Elasticity System

We study the properties of solutions of the mixed Dirichlet–Robin and Neumann–Robin problems for the linear system of elasticity theory in the exterior of a compact set and the asymptotic behavior of solutions of these problems at infinity under the assumption that the energy integral with weight | x | a is finite for such solutions. We use the variational principle and depending on the value of the parameter a, obtain uniqueness (non-uniqueness) theorems of the mixed problems or present exact formulas for the dimension of the space of solutions.

Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

2014 ◽  
Vol 58 (1) ◽  
pp. 183-197 ◽  
Author(s):  
John R. Graef ◽  
Johnny Henderson ◽  
Rodrica Luca ◽  
Yu Tian
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Boundary Value Problems ◽  
Order Differential Equation ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Optimal Length ◽  
The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

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