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Unbounded solutions of BVP for second order ODE with p -Laplacian on the half line

Yuji Liu, Patricia J. Y. Wong (2013)

Applications of Mathematics

By applying the Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three unbounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature.

Uniformly enclosing discretization methods and grid generation for semilinear boundary value problems with first order terms

Hans-Görg Roos (1989)

Aplikace matematiky

The paper deals with uniformly enclosing discretization methods of the first order for semilinear boundary value problems. Some fundamental properties of this discretization technique (the enclosing property, convergence, the inverse-monotonicity) are proved. A feedback grid generation principle using information from the lower and upper solutions is presented.

Unique solvability of a linear problem with perturbed periodic boundary values

Bahman Mehri, Mohammad H. Nojumi (1999)

Czechoslovak Mathematical Journal

We investigate the problem with perturbed periodic boundary values y ' ' ' ( x ) + a 2 ( x ) y ' ' ( x ) + a 1 ( x ) y ' ( x ) + a 0 ( x ) y ( x ) = f ( x ) , y ( i ) ( T ) = c y ( i ) ( 0 ) , i = 0 , 1 , 2 ; 0 < c < 1 with a 2 , a 1 , a 0 C [ 0 , T ] for some arbitrary positive real number T , by transforming the problem into an integral equation with the aid of a piecewise polynomial and utilizing the Fredholm alternative theorem to obtain a condition on the uniform norms of the coefficients a 2 , a 1 and a 0 which guarantees unique solvability of the problem. Besides having theoretical value, this problem has also important applications since decay is a phenomenon that all...

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