Convex radial solutions for Monge-Amp$ \grave{\text e} $re equations involving the gradient

Abstract

<abstract><p>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 $:</p> <p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{cases} \det (D^2u) = f(|x|, -u, |\nabla u|), x\in B, \\ u|_{\partial B} = 0, \end{cases} $\end{document} </tex-math></disp-formula></p> <p>where $ B: = \{x\in \mathbb R^N: |x| < 1\} $. The fixed point index theory is employed in the proofs of the main results.</p></abstract>