We prove the existence of multiple positive solutions for elliptic systems with linear boundary conditions of Neumann type. We suppose that the nonlinearities grow quadratically with respect to gradient. A key step is to obtain a priori bound on the derivatives by using a Gronwall-type inequality. Our approach is topological and relies on the fixed point index.
Radial solutions for a Neumann elliptic system with quadratic growth in the gradient
filomena cianciaruso;paolamaria pietramala
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Abstract
We prove the existence of multiple positive solutions for elliptic systems with linear boundary conditions of Neumann type. We suppose that the nonlinearities grow quadratically with respect to gradient. A key step is to obtain a priori bound on the derivatives by using a Gronwall-type inequality. Our approach is topological and relies on the fixed point index.File in questo prodotto:
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