A class of positive linear operators and applications to nonlinear boundary value problems
Keywords
Positive linear operator, fixed point index, positive solution, nonlocal boundary value problemAbstract
We discuss the class of $u_0$-positive linear operators relative to two cones and use a comparison theorem for this class to give some short proofs of new fixed point index results for some nonlinear operators that arise from boundary value problems. In particular, for some types of boundary conditions, especially nonlocal ones, we obtain a new existence result for multiple positive solutions under conditions which depend solely on the positive eigenvalue of a linear operator. We also treat some problems where the nonlinearity $f(t,u)$ is singular at $u=0$.Downloads
Published
2012-04-23
How to Cite
1.
WEBB, Jeffrey R. L. A class of positive linear operators and applications to nonlinear boundary value problems. Topological Methods in Nonlinear Analysis. Online. 23 April 2012. Vol. 39, no. 2, pp. 221 - 242. [Accessed 19 April 2024].
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