| Volume 1, Number 1, 2011, Pages 21-32 DOI：10.11948/2011003 |
| Existence of nonzero positive solutions of systems of second order |
| Kunquan Lan |
| Keywords:Systems of elliptic boundary value problems, fixed point equations, fixed point index. |
| Abstract: |
| Existence of nonzero positive solutions of systems of second order elliptic boundary value problems under sublinear conditions is obtained. The methodology is to establish a new result on existence of nonzero positive solutions of a fixed point equation in real Banach spaces by using the well-known theory of fixed point index for compact maps defined on cones, where the fixed point equation involves composition of a compact linear operator and a continuous nonlinear map. The conditions imposed on the nonlinear maps involve the spectral radii of the compact linear operators. Moreover, the nonlinear maps are not required to be increasing in ordered Banach spaces. |
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