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.
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Vazquez, J.L. Existence and regularity of solutions for a semilinear first-order equation on the torus. Manuscripta Math 45, 193–206 (1984). https://doi.org/10.1007/BF01169773
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DOI: https://doi.org/10.1007/BF01169773