Abstract
The existence of at least one periodic solution of a very general second order nonlinear parabolic boundary value problem is proved under the assumption that a lower solution ϕ and an upper solution ψ with ϕ≦ψ are known.
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H. Amann,Periodic solutions of semi-linear parabolic equations, to appear in a volume on “Nonlinear Analysis” dedicated to Professor Rothe on the occasion of his 80th birthday, 1976.
F. E. Browder,Existence theorems for nonlinear partial differential equations, Proc. Sympos. Pure Math., Vol. 16, Amer. Math. Soc., Providence, Rhode Island, 1970 pp. 1–60.
J. Deuel,Nichtlineare parabolische Randwertprobleme mit Unter- und Oberlöungen, ETH Diss. Nr. 5750, Zurich, 1976.
J. Deuel and P. Hess,A criterion for the existence of solutions of nonlinear elliptic boundary value problems. Proc. Roy. Soc. Edinburgh Sect. A74 (1975), 49–54.
P. Hess,On the solvability of nonlinear elliptic boundary value problems, Indiana Univ. Math. J.25 (1976), 461–466.
J.-L. Lions,Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Gauthiers-Villars, Paris, 1969.
J.-P. Puel,Existence, comportement à l'infini et stabilité dans certains problèmes quasilinéaires elliptiques et paraboliques d'ordre 2, Ann. Scuola Norm. Sup. Pisa,3 (1976), 89–119.
D. H. Sattinger,Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J.21 (1972), 979–1000.
P. E. Sobolevskii, Equations of parabolic type in a Banach space, Amer. Math. Soc. Transl., Ser. 2,49 (1966), 1–62.
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Deuel, J., Hess, P. Nonlinear parabolic boundary value problems with upper and lower solutions. Israel J. Math. 29, 92–104 (1978). https://doi.org/10.1007/BF02760403
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DOI: https://doi.org/10.1007/BF02760403