Nonconstant radial positive solutions of elliptic systems with Neumann boundary conditions

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• 作者：Ruyun Ma^a ; ¹ ; ^{mary@nwnu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Tianlan Chen^a ; ^{chentianlan511@126.com" class="auth_mail" title="E-mail the corresponding author} ; Haiyan Wang^b ; ^{Haiyan.Wang@asu.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Radial eigenvalue ; Neumann problem ; Nonconstant radial solutions ; Bifurcation ; Perron&ndash ; Frobenius Theorem
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 November 2016
• 年：2016
• 卷：443
• 期：1
• 页码：542-565
• 全文大小：433 K

文摘

Let class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16301913&_mathId=si1.gif&_user=111111111&_pii=S0022247X16301913&_rdoc=1&_issn=0022247X&md5=1ae759d167975db0d86de7bf20fdbaba" title="Click to view the MathML source">B_Rclass="mathContainer hidden">class="mathCode">$B_R$ be the ball of radius R   in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16301913&_mathId=si2.gif&_user=111111111&_pii=S0022247X16301913&_rdoc=1&_issn=0022247X&md5=5cf7f9ac3fbbad299a864af601681500" title="Click to view the MathML source">R^Nclass="mathContainer hidden">class="mathCode">${\mathbb{R}}^N$ with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16301913&_mathId=si3.gif&_user=111111111&_pii=S0022247X16301913&_rdoc=1&_issn=0022247X&md5=f174e063c5921d90c548055b91cbefa1" title="Click to view the MathML source">N≥2class="mathContainer hidden">class="mathCode">$N\ge 2$. We consider the nonconstant radial positive solutions of elliptic systems of the form where f and g are nondecreasing in each component. With few assumptions on the nonlinearities, we apply bifurcation theory to show the existence of at least one nonnegative, nonconstant and nondecreasing solution.