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Solutions to some nonlinear PDE's in the form of Laplace type integrals

Maria E. Pliś (2002)

Annales Polonici Mathematici

A nonlinear equation P ( D ) u = α u m in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of Char P, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.

Some commutative neutrix convolution products of functions

Brian Fisher, Adem Kiliçman (1995)

Commentationes Mathematicae Universitatis Carolinae

The commutative neutrix convolution product of the locally summable functions cos - ( λ x ) and cos + ( μ x ) is evaluated. Further similar commutative neutrix convolution products are evaluated and deduced.

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