Semilinear elliptic equations in R(N) with almost periodic or unbounded forcing term

Fournier, G.;Szulkin, A;Willem, Michel
(1996) SIAM Journal on Mathematical Analysis — Vol. 27, n° 6, p. 1653-1660 (1996)

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  • Fournier, G.
    Author
  • Szulkin, A
    Author
  • Willem, MichelUCLouvain
    Author
Abstract
This work is devoted to the existence and uniqueness of almost periodic solutions in R(N) of the equation -Delta u + Sigma(j=1)(N) c(j) partial derivative(j)u + g(u) = h(x). We also prove the existence of solutions with the same growth as some unbounded forcing terms. Under a local monotonicity assumption, the method of upper and lower solutions is used.
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Fournier, G., Szulkin, A., & Willem, M. (1996). Semilinear elliptic equations in R(N) with almost periodic or unbounded forcing term. SIAM Journal on Mathematical Analysis, 27(6), 1653-1660. https://doi.org/10.1137/S0036141094278699 (Original work published 1996)