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Existence and L∞ estimates for a class of singular ordinary differential equations

Published online by Cambridge University Press:  17 April 2009

J. M. Gomes
J. M. Gomes
Affiliation:
CMAF-Faculdade de Ciências da Universidade de Lisboa, Avenida Professor Gama Pinto, 2, 1649–003 Lisboa, Portugal, e-mail: [email protected]
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We prove the existence of a positive solution to an equation of the form (1/Φ(t)) (Φ(t)u′(t))′ = f(u(t)) with Dirichlet conditions where the friction term Φ′/Φ is increasing. Our method combines variational and topological arguments and provides an L∞ estimate of the solution.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 70 , Issue 3 , December 2004 , pp. 429 - 440
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Agarwal, R., ORegan, D. and Wong, P., Positive solutions of differential, difference and integral equations (Kluwer Academic Publishers, Dordrecht, 1999).CrossRefGoogle Scholar
[2]Berestycki, H., Lions, P.L. and Peletier, L.A., ‘An ODE approach to the existence of positive solutions for semilinear problems in ℝn’, Indiana Univ. Math. J. 30 (1981), 141–157.CrossRefGoogle Scholar
[3]Bobisud, L.E. and O'Regan, D., ‘Positive solutions for a class of nonlinear singular boundary value problems at resonance’, J. Math. Anal. Appl. 184 (1994), 263–284.CrossRefGoogle Scholar
[4]O'Regan, D., Solvability of some two point boundary value problems of Dirichlet, Neumann, or periodic type, Dynam. Systems Appl. 2 (1993), 163–182.Google Scholar
[5]O'Regan, D., ‘Nonresonance and existence for singular boundary value problems’, Nonlinear Anal. 23 (1994), 165–186.CrossRefGoogle Scholar
[6]Rabinowitz, P.H., Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Series in Math. 65 (Amer. Math. Soc., Providence R.I., 1986).CrossRefGoogle Scholar