Displaying similar documents to “The exact asymptotic behaviour of the unique solution to a singular Dirichlet problem.”

Decaying Regularly Varying Solutions of Third-order Differential Equations with a Singular Nonlinearity

Ivana Kučerová (2014)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper is concerned with asymptotic analysis of strongly decaying solutions of the third-order singular differential equation x ' ' ' + q ( t ) x - γ = 0 , by means of regularly varying functions, where γ is a positive constant and q is a positive continuous function on [ a , ∞ ) . It is shown that if q is a regularly varying function, then it is possible to establish necessary and sufficient conditions for the existence of slowly varying solutions and regularly varying solutions of (A) which decrease to 0 as t → ∞ and...

Asymptotic analysis of positive solutions of generalized Emden-Fowler differential equations in the framework of regular variation

Jaroslav Jaroš, Kusano Takaŝi, Jelena Manojlović (2013)

Open Mathematics

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Positive solutions of the nonlinear second-order differential equation ( p ( t ) | x ' | α - 1 x ' ) ' + q ( t ) | x | β - 1 x = 0 , α > β > 0 , are studied under the assumption that p, q are generalized regularly varying functions. An application of the theory of regular variation gives the possibility of obtaining necessary and sufficient conditions for existence of three possible types of intermediate solutions, together with the precise information about asymptotic behavior at infinity of all solutions belonging to each type of solution classes. ...