10,368 research outputs found
Multiple Positive solutions of a -Laplacian system with nonlinear BCs
Using the theory of fixed point index, we discuss existence, non-existence,
localization and multiplicity of positive solutions for a -Laplacian
system with nonlinear Robin and/or Dirichlet type boundary conditions. We give
an example to illustrate our theory.Comment: arXiv admin note: text overlap with arXiv:1408.017
Non-trivial, non-negative periodic solutions of a system of singular-degenerate parabolic equations with nonlocal terms
We study the existence of non-trivial, non-negative periodic solutions for
systems of singular-degenerate parabolic equations with nonlocal terms and
satisfying Dirichlet boundary conditions. The method employed in this paper is
based on the Leray-Schauder topological degree theory. However, verifying the
conditions under which such a theory applies is more involved due to the
presence of the singularity. The system can be regarded as a possible model of
the interactions of two biological species sharing the same isolated territory,
and our results give conditions that ensure the coexistence of the two species.Comment: 39 page
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