Existence of positive solutions to semilinear elliptic systems with supercritical growth

Li Congming; Villavert John

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Existence of positive solutions to semilinear elliptic systems with supercritical growth

机译：具有超临界增长的半线性椭圆系统正解的存在性

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We establish the existence of positive entire solutions to cooperative systems of semilinear elliptic equations involving nonlinearities with critical and supercritical growth. Consequently, we obtain existence results to several well-known model examples such as systems of the Hnon, Lane-Emden, and stationary Schrodinger types. The main technique for generating our results relies on a topological approach for the shooting method combined with nonexistence results to closely related boundary value problems.

机译：我们建立了具有临界和超临界增长非线性的半线性椭圆方程合作系统正整体解的存在性。因此，我们获得了一些知名模型实例的存在结果，例如Hnon，Lane-Emden和平稳Schrodinger类型的系统。产生结果的主要技术依赖于射击方法的拓扑方法，结合不存在的结果来解决紧密相关的边值问题。

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《Communications in Partial Differential Equations》 |2016年第9期|共11页
作者
Li Congming; Villavert John;
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正文语种 eng
中图分类偏微分方程;
关键词
Degree theory; entire solutions; existence theory; Henon system; Lane-Emden system; Schrodinger system; shooting method;

机译：度论;整体解;存在论;Henon系统;Lane-Emden系统;Schrodinger系统;射击方法;

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专利

1. Existence of positive solutions to semilinear elliptic systems with supercritical growth [J] . Li Congming, Villavert John Communications in Partial Differential Equations . 2016,第7a9期

机译：具有超临界增长的半线性椭圆系统正解的存在性
2. Large positive solutions of semilinear elliptic equations with critical and supercritical growth [J] . Guo ZM., Zhang H. Journal of Mathematical Analysis and Applications . 2002,第1期

机译：具有临界和超临界增长的半线性椭圆方程的大正解
3. On the existence of positive solutions to semilinear elliptic systems involving gradient term [J] . Abdellaoui Boumediene, Attar Ahmed, Laamri El-Haj Applicable Analysis . 2019,第5a8期

机译：关于涉及梯度术语的半线性椭圆体系积极解决方案的存在
4. Existence of nontrivial positive solutions to a semilinear elliptic system with variable coefficients [C] . Dawei Sun, Jiarui Liu International Conference on Mechanical Engineering and Green Manufacturing (MEGM 2012) . 2012

机译：具有变系数的半线性椭圆系统的非竞争正解的存在
5. Existence and bifurcation of multiple positive solutions for some semilinear elliptic equations. [D] . Zhao, Xuejin. 1998

机译：一类半线性椭圆型方程的多个正解的存在性和分歧。
6. Existence and stability of stationary solutions to spatially extended autocatalytic and hypercyclic systems under global regulation and with nonlinear growth rates [O] . Alexander S. Bratus, Vladimir P. Posvyanskii, Artem S. Novozhilov -1

机译：全球调节下空间扩展自催化和高循环系统及非线性增长的存在与稳定性
7. Existence of positive solutions for a class of semilinear and quasilinear elliptic equations with supercritical case [O] . Gao Juanjuan, Zhang Yong, Zhao Peihao 2011

机译：一类超临界情形的半线性和拟线性椭圆型方程正解的存在性
8. On the Existence of Positive Solutions of Semilinear Elliptic Equations [R] . Lions, P. L. 1981

机译：关于半线性椭圆型方程正解的存在性

Existence of positive solutions to semilinear elliptic systems with supercritical growth

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