A family of formal solutions of some type of nonlinear partial differential equations is found. Terms of such solutions are Laplace transforms of some Laplace distributions. The series of these distributions are locally finite.
@article{bwmeta1.element.bwnjournal-article-apmv69z2p99bwm, author = {Maria E. Pli\'s}, title = {Poincar\'e theorem and nonlinear PDE's}, journal = {Annales Polonici Mathematici}, volume = {69}, year = {1998}, pages = {99-105}, zbl = {1101.35308}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv69z2p99bwm} }
Maria E. Pliś. Poincaré theorem and nonlinear PDE's. Annales Polonici Mathematici, Tome 69 (1998) pp. 99-105. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv69z2p99bwm/
[000] [1] V. I. Arnold, Additional Topics in the Theory of Ordinary Differential Equations, Nauka, Moscow, 1978 (in Russian).
[001] [2] A. Bobylev, Poincaré theorem, Boltzmann equation and KdV-type equations, Dokl. Akad. Nauk SSSR 256 (1981), 1341-1346 (in Russian).
[002] [3] R. R. Rosales, Exact solutions of some nonlinear evolution equations, Stud. Appl. Math. 59 (1978), 117-151. | Zbl 0387.35061
[003] [4] Z. Szmydt and B. Ziemian, Laplace distributions and hyperfunctions on ℝ̅ⁿ₊, J. Math. Sci. Tokyo 5 (1998), 41-74.
[004] [5] B. Ziemian, Generalized analytic functions with applications to singular ordinary and partial differential equations, Dissertationes Math. 354 (1996).