Monotonicity and nonexistence of positive solutions for pseudo-relativistic equation with indefinite nonlinearity

Communications on Pure & Applied Analysis Pub Date : 1900-01-01 DOI:10.3934/cpaa.2022037

Yuxia Guo, Shaolong Peng

引用次数: 3

Abstract

In this paper, we consider the following general pseudo-relativistic Schrödinger equation with indefinite nonlinearities:

\begin{document}$ (-\Delta+m^{2})^{s}u = a(x_1)f\left(u,\nabla u\right),\quad {\rm{in}} \,\,\mathbb R^{N}, $\end{document}

where \begin{document}$ s\in(0,1) $\end{document}, mass \begin{document}$ m>0 $\end{document} and \begin{document}$ a $\end{document} is a non-decreasing functions. We prove the nonexistence and the monotonicity of the positive bounded solution for the above equation via the direct method of moving planes.

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不定非线性伪相对论方程正解的单调性和不存在性

In this paper, we consider the following general pseudo-relativistic Schrödinger equation with indefinite nonlinearities: \begin{document}$ (-\Delta+m^{2})^{s}u = a(x_1)f\left(u,\nabla u\right),\quad {\rm{in}} \,\,\mathbb R^{N}, $\end{document} where \begin{document}$ s\in(0,1) $\end{document}, mass \begin{document}$ m>0 $\end{document} and \begin{document}$ a $\end{document} is a non-decreasing functions. We prove the nonexistence and the monotonicity of the positive bounded solution for the above equation via the direct method of moving planes.

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications on Pure & Applied Analysis

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