This paper presents an abstract theory for the existence, localization and multiplicity of fixed points in a cone. The key assumption is the property of the nonlinear operator of satisfying an inequality of Harnack type. In particular, the theory offers a completely new approach to the problem of positive solutions of quasilinear elliptic equations with p-Laplace operator.
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania
Weak Harnack inequality; fixed point; fixed point index; p-Laplace operator; quasilinear elliptic equation.
R. Precup, Abstract weak Harnack inequality, multiple fixed points and p-Laplace equations, J. Fixed Point Theory Appl. 12 (2012), 193-206, https://doi.org/10.1007/s11784-012-0091-2
Journal of Fixed Point Theory and Applications
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