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, Volume 45, Issue 2, pp 193–206 | Cite as

Existence and regularity of solutions for a semilinear first-order equation on the torus

  • Juan L. Vazquez


The problem\(\sum {a_i \frac{{\partial u}}{{\partial x_i }} + g(x,u) = 0}\) is considered on the N-dimensional torus Ω with ai∈ℝ and g a continuous function satisfying a growth condition as ¦u¦→∞. We show the existence of bounded solutions that are continuous if g is strictly increasing in u.


Continuous Function Growth Condition Number Theory Algebraic Geometry Topological Group 
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    SCHOENENBERGER-DEUEL, I., and VAILLANCOURT, R.: Flots sur le tore bidimensionel. C.R. Acad. Sc. Paris286 A, 447–448 (1978)Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Juan L. Vazquez
    • 1
  1. 1.Division MatematicasUniv. AutonomaMadrid-34Spain

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