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manuscripta mathematica

, 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
Article
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Abstract

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.

Keywords

Continuous Function Growth Condition Number Theory Algebraic Geometry Topological Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    BREZIS, H., and NIRENBERG, L.: Some first-order nonlinear equations on a torus. Comm. Pure Applied Math.30,1–11 (1977)Google Scholar
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    EVANS, L.C.: Application of nonlinear semigroup theory to certain partial differential equations, in Nonlinear Evolution Equations, M. G. Crandall ed. New York: Academic Press 1978Google Scholar
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    FENICHEL, N.: Persistence and smoothness of invariant manifolds of flows. Indiana Univ. Math. Jour.21, 193–226 (1971)Google Scholar
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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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