A sub-supersolution method for nonlinear elliptic singular systems with natural growth and some applications

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• 作者：José ; Carmona^a ; ^{jcarmona@ual.es" class="auth_mail" title="E-mail the corresponding author} ; Pedro J. Martí ; nez-Aparicio^b ; ^{pedroj.martinez@upct.es" class="auth_mail" title="E-mail the corresponding author} ; Antonio Suá ; rez^c ; ^{suarez@us.es" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35B09 ; 35B51 ; 35D30 ; 35J60 ; 35J75 ; 92B05
• 刊名：Nonlinear Analysis
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：132
• 期：Complete
• 页码：47-65
• 全文大小：621 K

文摘

In this paper we give a sub-supersolution method for nonlinear elliptic singular systems with quadratic gradient whose model system is the following where Ω$\Omega$ is a smooth bounded domain of R^N${\mathbb{R}}^N$ (N≥3$N\ge 3$), 35d2c4684dcbd14f8c84c995b5dc7d4" title="Click to view the MathML source">β,μ≥0$\beta ,\mu \ge 0$, 0<α,γ<1$0<\alpha ,\gamma <1$ and regular f₁,f₂$f_1,f_2$ functions. Moreover, we apply it to prove existence of solution for some systems, including the classical Lotka–Volterra models with gradient terms. Specifically, we study the competition and the symbiotic Lotka–Volterra systems.