Displaying similar documents to “Existence and Uniqueness Theorem for Singular Initial Value Problems and Applications”

Solution of nonlinear singular initial value problems of generalized Lane-Emden type using block pulse functions in a large interval

M. H. Heydari, M. R. Hooshmandasl, F. Mohammadi, A. Ciancio (2016)

Waves, Wavelets and Fractals

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In this paper, the block pulse functions (BPFs) and their operational matrices of integration and differentiation are used to solve nonlinear singular initial value problems (NSIVPs) of generalized Lane-Emden type in a large interval. In the proposed method, we present a new technique for computing nonlinear terms in such equations. This technique is then utilized to reduce the solution of this nonlinear singular initial value problems to a system of nonlinear algebraic equation whose...

Singular Dirichlet Problems with Quadratic Gradient

Pedro J. Martínez-Aparicio (2009)

Bollettino dell'Unione Matematica Italiana

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We study the existence of solution for nonlinear elliptic problems with singular lower order terms that have natural growth with respect to the gradient.

Positive solutions to a singular fourth-order two-point boundary value problem

Qingliu Yao (2011)

Annales Polonici Mathematici

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This paper studies the existence of multiple positive solutions to a nonlinear fourth-order two-point boundary value problem, where the nonlinear term may be singular with respect to both time and space variables. In order to estimate the growth of the nonlinear term, we introduce new control functions. By applying the Hammerstein integral equation and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several local existence theorems are proved.

On complete solutions and complete singular solutions of second order ordinary differential equations

Masatomo Takahashi (2007)

Colloquium Mathematicae

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A complete solution of an implicit second order ordinary differential equation is defined by an immersive two-parameter family of geometric solutions on the equation hypersurface. We show that a completely integrable equation is either of Clairaut type or of first order type. Moreover, we define a complete singular solution, an immersive one-parameter family of singular solutions on the contact singular set. We give conditions for existence of a complete solution and a complete singular...

Existence and uniqueness for non-linear singular integral equations used in fluid mechanics

E. G. Ladopoulos, V. A. Zisis (1997)

Applications of Mathematics

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Non-linear singular integral equations are investigated in connection with some basic applications in two-dimensional fluid mechanics. A general existence and uniqueness analysis is proposed for non-linear singular integral equations defined on a Banach space. Therefore, the non-linear equations are defined over a finite set of contours and the existence of solutions is investigated for two different kinds of equations, the first and the second kind. Moreover, the existence of solutions...