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On the existence of Lipschitzian solution of a composite functional equation

Okrzesik J.

Demonstratio Mathematica

2006

Vol. 39, nr 1

97-100

There are presented conditions which guarantee the existence of a Lip- schitzian solution of the composite functional equation phi(x) = G (x,phi(H(x,phi(x)))) are presented.

Analytic solutions of a first order iterative differential equation x'(z)=x(p(z) + bx(z))

Qiu F., Liu H.

Demonstratio Mathematica

2006

Vol. 39, nr 1

81-90

This paper is concerned with a iterative differential equation x'{z) = x{p(z) + bx(z)). By constructing a convergent power series solution y(z) of a companion equation of the form betay'(3betaz) = y'(z)[y(beta2z) - p(y(betaz)]], analytic solutions of the form [y(betay- l(z)) - p(z)]/b for the original differential equation are obtained.