A class of positive linear operators and applications to nonlinear boundary value problems
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Positive linear operator, fixed point index, positive solution, nonlocal boundary value problemAbstrakt
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 $u=0$.Pobrania
Opublikowane
2012-04-23
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WEBB, Jeffrey R. L. A class of positive linear operators and applications to nonlinear boundary value problems. Topological Methods in Nonlinear Analysis [online]. 23 kwiecień 2012, T. 39, nr 2, s. 221–242. [udostępniono 23.9.2024].
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