Solutions to some nonlinear PDE's in the form of Laplace type integrals
Volume 79 / 2002
Annales Polonici Mathematici 79 (2002), 45-62
MSC: 35C10, 35C15, 44A10, 46F12
DOI: 10.4064/ap79-1-4
Abstract
A nonlinear equation $P(D)u=\alpha u^{m}$ in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of ${\rm Char}\hskip1pt P$, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.
