Multiple positive solutions of parabolic systems with nonlinear, nonlocal initial conditions
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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 non-existence result and an example to illustrate our theory.
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Cited by 2 Pith papers
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Existence of Positive Mild Eigenfunctions for Caputo Fractional Semilinear Evolution Equations with Nonlocal Initial Conditions
Positive mild eigenfunctions exist for Caputo fractional autonomous evolution equations with nonlocal initial conditions via the Birkhoff-Kellogg theorem applied to compact Mittag-Leffler operators in a positive cone.
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Existence of Positive Mild Eigenfunctions for Caputo Fractional Semilinear Evolution Equations with Nonlocal Initial Conditions
Existence of positive eigenpairs is established for Caputo fractional autonomous evolution equations with nonlocal initials by applying the Birkhoff-Kellogg theorem in cones to compact Mittag-Leffler operators.
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