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A semilinear elliptic problem which is not selfadjoint. (English) Zbl 0592.35052

In Fortsetzung einer früheren gemeinsamen Arbeit mit L. Cesari [Nonlinear Anal., Theory Methods Appl. 9, 1227-1241 (1985; Zbl 0535.35026)] betrachtet die Verf. ein speziell nicht-selbstadjungiertes Problem für die elliptische Gleichung \[ u_{xx}+u_{yy}+2\lambda^ 2u=f(x,y)+g(u). \] Sie fügt ebenfalls ein numerisches Beispiel an.
Reviewer: J.Appell

MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
47H10 Fixed-point theorems

Citations:

Zbl 0535.35026
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References:

[1] R. A. Adams, Sobolev Spaces, Academic Press, New York, 1975.
[2] L. Cesari, ”Nonlinear Analysis. New Arguments and Results”, Rend. Accad. Naz. Lincei, I and II. 76 (1984), 339–345; 77 (1984), 13–20.
[3] L. Cesari & T. T. Bowman, ”Existence of Solutions to Nonselfadjoint Boundary Value Problems for Ordinary Differential Equations”, Nonlinear Analysis, 9 (1985), 1211–1225. · Zbl 0569.34014 · doi:10.1016/0362-546X(85)90031-8
[4] L. Cesari & R. Kannan, ”Solutions of Nonlinear Hyperbolic Equations at Reson · Zbl 0495.35007 · doi:10.1016/0362-546X(82)90063-3
[5] L. Cesari & R. Kannan, ”Periodic Solutions of Nonlinear Wave Equations”, Arch · Zbl 0521.35037 · doi:10.1007/BF00250554
[6] L. Cesari & P. Pucci, Global Periodic Solutions of the Nonlinear Wave Equation, Archive Rational Mech. Anal., 89 (1985), 187–209. · Zbl 0579.35056 · doi:10.1007/BF00276871
[7] L. Cesari & P. Pucci, ”Existence Theorems for Nonselfadjoint Semilinear Elliptic Boundary Value Problems”, Nonlinear Analysis, 9 (1985), 1227–1241. · Zbl 0535.35026 · doi:10.1016/0362-546X(85)90032-X
[8] L. Tonelli, Serie Trigonometriche, Zanichelli, Bologna, 1928, viii + 526.
[9] A. Zygmund, Trigonometric Series, Vols. 1 and II, 2nd ed., Cambridge University Press, New York, 1959.
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