Differential and Integral Equations

Existence of solutions for elliptic systems with Hölder continuous nonlinearities

Manuel Delgado and Antonio Suárez

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In this work we prove the existence of solutions for an elliptic system between lower and upper solutions when the nonlinearities are Hölder continuous functions without a Lipschitz condition. Specifically, under appropriate conditions of monotony on the nonlinear reaction terms we introduce two monotone sequences which converge to a minimal and a maximal solution respectively. Finally, we apply these results to a dynamical population problem with "slow" diffusion.

Article information

Differential Integral Equations, Volume 13, Number 4-6 (2000), 453-477.

First available in Project Euclid: 21 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35J55
Secondary: 35B50: Maximum principles 47J05: Equations involving nonlinear operators (general) [See also 47H10, 47J25] 47N60: Applications in chemistry and life sciences 92D25: Population dynamics (general)


Delgado, Manuel; Suárez, Antonio. Existence of solutions for elliptic systems with Hölder continuous nonlinearities. Differential Integral Equations 13 (2000), no. 4-6, 453--477. https://projecteuclid.org/euclid.die/1356061235

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