Nonnegative solutions of the radial Laplacian with nonlinearity that changes sign
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- by N. P. Cac, A. M. Fink and J. A. Gatica
- Proc. Amer. Math. Soc. 123 (1995), 1393-1398
- DOI: https://doi.org/10.1090/S0002-9939-1995-1285979-9
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Abstract:
We find a solution to the radial Laplacian equation $y'' + \frac {{N - 1}}{x}y’ + \lambda a(x)f(y) = 0,y’ (0) = y(1) = 0$ when a may change sign and is "sufficiently positive". The function f is qualitatively like ${e^y}$, and we conclude solutions for $0 \leq \lambda \leq {\lambda _0}$.References
- A. M. Fink, Juan A. Gatica, Gastón E. Hernández, and Paul Waltman, Approximation of solutions of singular second order boundary value problems, SIAM J. Math. Anal. 22 (1991), no. 2, 440–462. MR 1084967, DOI 10.1137/0522029
- A. M. Fink, The radial Laplacian Gel′fand problem, Delay and differential equations (Ames, IA, 1991) World Sci. Publ., River Edge, NJ, 1992, pp. 93–98. MR 1170146, DOI 10.2307/3618995
- A. M. Fink, J. A. Gatica, and Gastón E. Hernández, Eigenvalues of generalized Gel′fand models, Nonlinear Anal. 20 (1993), no. 12, 1453–1468. MR 1225348, DOI 10.1016/0362-546X(93)90169-S
- N. P. Cac, A. M. Fink, and J. A. Gatica, Nonnegative solutions of quasilinear elliptic problems with nonnegative coefficients, J. Math. Anal. Appl. 206 (1997), no. 1, 1–9. MR 1429275, DOI 10.1006/jmaa.1997.4882
Bibliographic Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 1393-1398
- MSC: Primary 34B15; Secondary 35B05, 35J99
- DOI: https://doi.org/10.1090/S0002-9939-1995-1285979-9
- MathSciNet review: 1285979