In this paper, we study the existence, localization and multiplicity of positive solutions for parabolic systems with nonlocal initial conditions. In order to do this, we extend an abstract theory that was recently developed by the authors jointly with Radu Precup, related to the existence of fixed points of nonlinear operators satisfying some upper and lower bounds. Our main tool is the Granas fixed-point index theory. We also provide a nonexistence result and some examples to illustrate our theory.

Multiple positive solutions of parabolic systems with nonlinear, nonlocal initial conditions

INFANTE, GENNARO
;
2016

Abstract

In this paper, we study the existence, localization and multiplicity of positive solutions for parabolic systems with nonlocal initial conditions. In order to do this, we extend an abstract theory that was recently developed by the authors jointly with Radu Precup, related to the existence of fixed points of nonlinear operators satisfying some upper and lower bounds. Our main tool is the Granas fixed-point index theory. We also provide a nonexistence result and some examples to illustrate our theory.
Parabolic systems, Fixed point index, Nonlocal initial conditions
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/144022
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