On the number of positive solutions of nonlinear systems |
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Authors: | Haiyan Wang |
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Institution: | Department of Integrative Studies, Arizona State University West, PO Box 37100, Phoenix, AZ 85069, USA |
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Abstract: | We prove that appropriate combinations of superlinearity and sublinearity of with respect to at zero and infinity guarantee the existence, multiplicity, and nonexistence of positive solutions to boundary value problems for the n-dimensional system 0<t<1. The vector-valued function is defined by where and ? covers the two important cases ?(u′)=u′ and ?(u′)=|u′|p−2u′, p>1. Our methods employ fixed point theorems in a cone. |
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