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Boundary estimates for solutions of weighted semilinear elliptic equations
Coercivity of elliptic mixed boundary value problems in annulus of $\mathbb{R}^N$
1. | Departamento de Matemática Aplicada y Computación, Escuela Técnica Superior de Ingeniería - ICAI, Universidad Ponticia Comillas, Alberto Aguilera, 25, 28015-Madrid, Spain |
References:
[1] |
H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18 (1976), 620-709.
doi: 10.1137/1018114. |
[2] |
H. Amann, Dual semigroups and second order linear elliptic boundaryvalue problems, Israel J. Math., 45 (1983), 225-254.
doi: 10.1007/BF02774019. |
[3] |
H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinearindefinite elliptic problems, Journal of Differential Equations, 146 (1998), 336-374.
doi: 10.1006/jdeq.1998.3440. |
[4] |
S. Cano-Casanova and J. López-Gómez, Properties of the principal eigenvalues of a general classof non-classical mixed boundary value problems, Journal ofDifferential Equations, 178 (2002), 123-211.
doi: 10.1006/jdeq.2000.4003. |
[5] |
S. Cano-Casanova, Existence and structure of the set ofpositive solutions of a general class of sublinear elliptic non-classical mixedboundary value problems, Nonlinear Analysis, 49 (2002), 361-430.
doi: 10.1016/S0362-546X(01)00116-X. |
[6] |
C. Faber, Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicherSpannung die Kreisförmige den tiefsten Grundton gibt, Sitzungsber. Bayer. Akad. der Wiss. Math. Phys., (1923), 169-172. |
[7] |
J. M. Fraile, P. Koch Medina, J. López-Gómez and S.Merino, Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation, Journal of Differential Equations, 127 (1996), 295-319.
doi: 10.1006/jdeq.1996.0071. |
[8] |
E. Krahn, Uber eine von Rayleigh formulierte Minimale igenschaft des Kreises, Math. Ann., 91 (1925), 97-100.
doi: 10.1007/BF01208645. |
[9] |
J. López-Gómez and M. Molina-Meyer, The maximum principle for cooperative weakly coupledelliptic systems and some applications, Differential IntegralEquations, 7 (1994), 383-398. |
[10] |
J. López-Gómez, The maximum principle and the existence of principaleigenvalues for some linear weighted boundary value problems, Journal of Differential Equations, 127 (1996), 263-294.
doi: 10.1006/jdeq.1996.0070. |
[11] |
J. López-Gómez, "The Strong Maximum Principle," preprint, 2011. |
[12] |
E. M. Stein, "Singular Integrals of Differentiability Propertiesof Functions," Princeton Univ. Press, Princeton, NJ, 1970. |
show all references
References:
[1] |
H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18 (1976), 620-709.
doi: 10.1137/1018114. |
[2] |
H. Amann, Dual semigroups and second order linear elliptic boundaryvalue problems, Israel J. Math., 45 (1983), 225-254.
doi: 10.1007/BF02774019. |
[3] |
H. Amann and J. López-Gómez, A priori bounds and multiple solutions for superlinearindefinite elliptic problems, Journal of Differential Equations, 146 (1998), 336-374.
doi: 10.1006/jdeq.1998.3440. |
[4] |
S. Cano-Casanova and J. López-Gómez, Properties of the principal eigenvalues of a general classof non-classical mixed boundary value problems, Journal ofDifferential Equations, 178 (2002), 123-211.
doi: 10.1006/jdeq.2000.4003. |
[5] |
S. Cano-Casanova, Existence and structure of the set ofpositive solutions of a general class of sublinear elliptic non-classical mixedboundary value problems, Nonlinear Analysis, 49 (2002), 361-430.
doi: 10.1016/S0362-546X(01)00116-X. |
[6] |
C. Faber, Beweis, dass unter allen homogenen Membranen von gleicher Fläche und gleicherSpannung die Kreisförmige den tiefsten Grundton gibt, Sitzungsber. Bayer. Akad. der Wiss. Math. Phys., (1923), 169-172. |
[7] |
J. M. Fraile, P. Koch Medina, J. López-Gómez and S.Merino, Elliptic eigenvalue problems and unbounded continua of positive solutions of a semilinear elliptic equation, Journal of Differential Equations, 127 (1996), 295-319.
doi: 10.1006/jdeq.1996.0071. |
[8] |
E. Krahn, Uber eine von Rayleigh formulierte Minimale igenschaft des Kreises, Math. Ann., 91 (1925), 97-100.
doi: 10.1007/BF01208645. |
[9] |
J. López-Gómez and M. Molina-Meyer, The maximum principle for cooperative weakly coupledelliptic systems and some applications, Differential IntegralEquations, 7 (1994), 383-398. |
[10] |
J. López-Gómez, The maximum principle and the existence of principaleigenvalues for some linear weighted boundary value problems, Journal of Differential Equations, 127 (1996), 263-294.
doi: 10.1006/jdeq.1996.0070. |
[11] |
J. López-Gómez, "The Strong Maximum Principle," preprint, 2011. |
[12] |
E. M. Stein, "Singular Integrals of Differentiability Propertiesof Functions," Princeton Univ. Press, Princeton, NJ, 1970. |
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