On a generalized nonlinear functional equation

The continuous small amplitude disturbances generated by the oscillations of a piston in a gas contained in a closed-ended tube are discussed. The coupled characteristic equations are integrated exactly for a model equation of state which approximates any stress–strain law with an error at O ([strain] 3 ). When the small amplitude limit is taken and the relative importance of amplitude dispersion and nonlinear interaction is assessed, the disturbances can be determined from solutions to a nonlinear functional equation. The motions are characterized by a similarity parameter, A , and a frequency parameter, ∆ . A simple algebraic scheme for constructing continuous periodic solutions of the functional equation is given, and the A–∆ plane is divided by a transition curve. The various resonances are then evident.

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Existence and uniqueness of BC [a,b] solutions of nonlinear functional equation

Demonstratio Mathematica ◽

10.1515/dema-1993-0107 ◽

1993 ◽

Vol 26 (1) ◽

Author(s):

Tadeusz Kostrzewskl

Keyword(s):

Functional Equation ◽

Existence And Uniqueness ◽

Nonlinear Functional Equation ◽

Nonlinear Functional

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On a special nonlinear functional equation

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1981.0146 ◽

1981 ◽

Vol 378 (1773) ◽

pp. 155-178 ◽

Cited By ~ 5

Keyword(s):

Functional Equation ◽

Infinite Sequence ◽

Analytic Solutions ◽

The Other ◽

Branch Points ◽

Natural Boundary ◽

Nonlinear Functional Equation ◽

Nonlinear Functional ◽

Change Of Variable ◽

The Difference

We study analytic solutions of the functional equation h(z) 2 – h(z 2 ) + c = 0, (H) where c > 0 is a parameter, and constant solutions are excluded. It suffices to consider solutions for which h(z) – z -1 is regular in a neighbourhood of z = 0. If 0 < c ≼ ¼, h(z) can be continued as a single-valued analytic function into the unit disc | z | < 1 where its only singularity is the pole at z = 0; the circle | z | = 1 is a natural boundary. On the other hand, if c > ¼, then by analytic continuation h(z) becomes a multiple-valued function with an infinite sequence of quadratic branch points tending to every point of | z | = 1, and no branch of h(z) can be continued beyond this circle. A change of variable transforms (H) into the difference equation g ( Z + 1) – g(Z) = g(Z) 2 + C , where C is a real parameter. The solutions of this equation have properties similar to thóse of (H).

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Solution of a Nonlinear Functional Equation

Sultan Qaboos University Journal for Science [SQUJS] ◽

10.24200/squjs.vol9iss0pp25-31 ◽

2004 ◽

Vol 9 ◽

pp. 25

Author(s):

Valery C. Covachev ◽

H. Ali Yurtsever

Keyword(s):

Functional Equation ◽

Matrix Method ◽

Functional Equations ◽

Linear Functional ◽

Parametric Approach ◽

Nonlinear Functional Equation ◽

Nonlinear Functional ◽

Linear Functional Equations

In the present paper a generalization of a theorem of I.B. Risteski (2004) concerning the solution of a nonlinear functional equation is given. The proof is based on a parametric approach by introducing a parameter in an arbitrary set , and on a matrix method for solving linear functional equations.

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