JournalsprimsVol. 43, No. 4pp. 923–943

Convergent and Divergent Solutions of Singular Partial Differential Equations with Resonance or Small Denominators

  • Masafumi Yoshino

    Hiroshima University, Japan
Convergent and Divergent Solutions of Singular Partial Differential Equations with Resonance or Small Denominators cover

Abstract

We show the solvability and nonsolvability of a singular nonlinear system of partial differential equations with resonance in a class of functions holomorphic in some neighborhood of the origin. These results are applied to the normal form theory of a singular vector field.

Cite this article

Masafumi Yoshino, Convergent and Divergent Solutions of Singular Partial Differential Equations with Resonance or Small Denominators. Publ. Res. Inst. Math. Sci. 43 (2007), no. 4, pp. 923–943

DOI 10.2977/PRIMS/1201012374