Abstract
In this paper two optimal inequalities are proven for the critical value λ* of the semilinear boundary value problem Δu+λf(u) = 0in Ω⊂M, u= 0 on ∂Ω. Here M is a two-dimensional Riemannian manifold with positive Gaussian curvature.
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References
H. Amann, Fixed points equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev. 18 (1976), 620–709.
P.L. Lions, On the Existence of Positive Solutions of Semilinear Elliptic Equations, SIAM Rev. 24 (1982), 441–467.
L.E. Payne, Bounds for solutions of a class of quasilinear elliptic boundary value problems in terms of the torsion function, Proc. Roy. Soc. Edinburgh 88a (1981), 251–256.
R.P. Sperb, Isoperimetric Ineqalities in a Boundary Value Problem on a Riemannian Manifold, J. of Appl. Math. & Phys. (ZAMP) 31 (1981), 740–753.
R.P. Sperb, Maximum Principles and their Applications, Math, in Science & Eng. 157, Academic Press, New York 1981.
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© 1987 Birkhäuser Verlag Basel
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Sperb, R.P. (1987). Optimal Bounds for the Critical Value in a Semilinear Boundary Value Problem on a Surface. In: Walter, W. (eds) General Inequalities 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik Série internationale d’Analyse numérique, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7192-1_31
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DOI: https://doi.org/10.1007/978-3-0348-7192-1_31
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7194-5
Online ISBN: 978-3-0348-7192-1
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