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Solutions to some nonlinear PDE's in the form of Laplace type integrals
2002
Annales Polonici Mathematici
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A nonlinear equation P (D)u = αu 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. 2000 Mathematics Subject Classification: 35C10, 35C15, 44A10, 46F12.
doi:10.4064/ap79-1-4
fatcat:3o7abjcazzfw7boutsiropoinm