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Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator

  • * Corresponding author: Ravi P. Agarwal

    * Corresponding author: Ravi P. Agarwal 

All authors equally contributed this manuscript

This work is supported by NSFC (No.11501342), NSF of Shanxi, China (No.201701D221007), Science and Technology Innovation Project of Shanxi Normal University (No.2019XSY027), the Graduate Innovation Program of Shanxi, China (No.2020SY337) and STIP (Nos.201802068 and 201802069)

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  • In this paper, we study the positive solutions of the Schrödinger elliptic system

    $ \begin{equation*} \begin{split} \left\{\begin{array}{ll}{\operatorname{div}(\mathcal{G}(|\nabla y|^{p-2})\nabla y) = b_{1}(|x|) \psi(y)+h_{1}(|x|) \varphi(z),}& {x \in \mathbb{R}^{n}(n \geq 3)}, \\ {\operatorname{div}(\mathcal{G}(|\nabla z|^{p-2})\nabla z) = b_{2}(|x|) \psi(z)+h_{2}(|x|) \varphi(y),} & {x \in \mathbb{R}^{n}},\end{array}\right. \end{split} \end{equation*} $

    where $ \mathcal{G} $ is a nonlinear operator. By using the monotone iterative technique and Arzela-Ascoli theorem, we prove that the system has the positive entire bounded radial solutions. Then, we establish the results for the existence and nonexistence of the positive entire blow-up radial solutions for the nonlinear Schrödinger elliptic system involving a nonlinear operator. Finally, three examples are given to illustrate our results.

    Mathematics Subject Classification: Primary: 35A24, 35B09; Secondary: 35B44.


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