This paper deals with the existence and multiplicity of convex radial solutions for the Monge-Amp$ \grave{\text e} $re equation involving the gradient $ \nabla u $:
$ \begin{cases} \det (D^2u) = f(|x|, -u, |\nabla u|), x\in B, \\ u|_{\partial B} = 0, \end{cases} $
where $ B: = \{x\in \mathbb R^N: |x| < 1\} $. The fixed point index theory is employed in the proofs of the main results.
Citation: Zhilin Yang. Convex radial solutions for Monge-Amp$ \grave{\text e} $re equations involving the gradient[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 20959-20970. doi: 10.3934/mbe.2023927
This paper deals with the existence and multiplicity of convex radial solutions for the Monge-Amp$ \grave{\text e} $re equation involving the gradient $ \nabla u $:
$ \begin{cases} \det (D^2u) = f(|x|, -u, |\nabla u|), x\in B, \\ u|_{\partial B} = 0, \end{cases} $
where $ B: = \{x\in \mathbb R^N: |x| < 1\} $. The fixed point index theory is employed in the proofs of the main results.
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Zhilin Yang. Convex radial solutions for Monge-Amp$ \grave{\text e} $re equations involving the gradient[J]. Mathematical Biosciences and Engineering, 2023, 20(12): 20959-20970. doi: 10.3934/mbe.2023927
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