A proof of a conjecture on the multiplicity of positive solutions of an indefinite superlinear problem
Guglielmo Feltrin, Juli\'an L\'opez-G\'omez, Juan Carlos Sampedro
TL;DR
This paper confirms a long-standing conjecture by proving that a specific class of indefinite superlinear boundary value problems has multiple positive solutions, advancing understanding in nonlinear differential equations.
Contribution
It provides a positive proof of a conjecture from 2000 about the multiplicity of positive solutions in superlinear indefinite boundary value problems.
Findings
Confirmed the conjecture on multiple positive solutions.
Established conditions under which solutions exist.
Enhanced understanding of indefinite superlinear problems.
Abstract
This paper solves in a positive manner a conjecture stated in 2000 by R. G\'omez-Re\~nasco and J. L\'opez-G\'omez regarding the multiplicity of positive solutions of a paradigmatic class of superlinear indefinite boundary value problems.
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Taxonomy
TopicsNonlinear Differential Equations Analysis · Differential Equations and Boundary Problems · advanced mathematical theories