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Existence and Uniqueness of Positive Radial Solutions for the Lane–Emden System
Nonlinear Analysis: Theory, Methods & Applications, 2004 The author studies the existence and the uniqueness of positive radial solutions of the semilinear elliptic Lane-Emden-type system with homogeneous Dirichlet data \[ \begin{cases} \Delta u+v^q=0 & \text{in } B_R, \\ \Delta v+u^p=0 & \text{in } B_R, \\ u=v=0 & \text{on } \partial B_R, \end{cases} \] where \(B_R\) denotes the open ball of radius \(R\) at
Robert Dalmasso
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Positive radial solutions for a class of (p, q) Laplacian in a ball
Positivity, 2022The authors are concerned with the Dirichlet problem \[ \begin{cases} -\Delta_pu-\Delta_qu=\lambda f(u) \text{ in }\Omega, \\ u=0 \text{ on }\Omega, \end{cases} \] where \(\Delta_ru=\operatorname{div}(\vert\nabla u\vert^{r-2}\nabla u)\) is the \(p\)-Laplacian, \(\Omega\) is the unit open ball, and \(p>q>1\).
D. Hai, R. Shivaji, X. Wang
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