Existence of solutions for semilinear problems with prescribed number of zeros on exterior domains

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• 作者：Joseph A. Iaia ^{iaia@unt.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Exterior domain ; Superlinear ; Radial
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：591-604
• 全文大小：371 K

文摘

In this paper we prove the existence of an infinite number of radial solutions of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si1.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=4df44eea5500a3fb78e676f68811b2e1" title="Click to view the MathML source">Δu+K(r)f(u)=0class="mathContainer hidden">class="mathCode">$\mathrm{\Delta }u+K(r)f(u)=0$ on the exterior of the ball of radius R   centered at the origin in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si2.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=9e8aadf101da4847ace01df320f3731e" title="Click to view the MathML source">R^Nclass="mathContainer hidden">class="mathCode">${\mathbb{R}}^N$ such that class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si3.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=f7f3751aefa14335daabd238d13c4aec">class="imgLazyJSB inlineImage" height="22" width="95" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0022247X16304954-si3.gif">class="mathContainer hidden">class="mathCode">$\underset{r\to \infty }{\lim }u(r)=0$ with prescribed number of zeros where class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si4.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=ef9d9b2f03042ad8c49767bc6e64473b" title="Click to view the MathML source">f:R→Rclass="mathContainer hidden">class="mathCode">$f:\mathbb{R}\to \mathbb{R}$ is odd and there exists a class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si5.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=177c3d829046d3a6603666c53964c567" title="Click to view the MathML source">β>0class="mathContainer hidden">class="mathCode">$\beta >0$ with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si6.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=5fdaef43fe99c7c7284fe8cd409aa19b" title="Click to view the MathML source">f<0class="mathContainer hidden">class="mathCode">$f<0$ on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si7.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=4c4776e9bb7d9588ab7578af89ec4da5" title="Click to view the MathML source">(0,β)class="mathContainer hidden">class="mathCode">$(0,\beta )$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si8.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=76fee739318e67a493cf1197d807c986" title="Click to view the MathML source">f>0class="mathContainer hidden">class="mathCode">$f>0$ on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si9.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=de60e152b9087654428a30e310b9225d" title="Click to view the MathML source">(β,∞)class="mathContainer hidden">class="mathCode">$(\beta ,\infty )$ with f superlinear for large u  , and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si10.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=206e25ed3fa52672e71f067b78d4808c" title="Click to view the MathML source">K(r)∼r^−αclass="mathContainer hidden">class="mathCode">$K(r)\sim r^{-\alpha }$ with class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16304954&_mathId=si11.gif&_user=111111111&_pii=S0022247X16304954&_rdoc=1&_issn=0022247X&md5=9bb2d361fd1b7f16bc10b251c12e8ad0" title="Click to view the MathML source">0<α<Nclass="mathContainer hidden">class="mathCode">$0<\alpha <N$.