Infinitely many nodal solutions for semilinear Robin problems with an indefinite linear part

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• 作者：Nikolaos S. Papageorgiou^a ; ^{npapg@math.ntua.gr" class="auth_mail" title="E-mail the corresponding author} ; Vicenţiu D. Rădulescu^b ; ^c ; ^{vicentiu.radulescu@imar.ro" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Indefinite potential ; Regularity theory ; Nodal solutions ; Carathé ; odory reaction ; Superlinear near zero ; Robin boundary condition
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：64
• 期：Complete
• 页码：42-50
• 全文大小：767 K

文摘

We consider a semilinear Robin problem driven by the Laplacian plus an indefinite potential and with a Carathéodory reaction n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302464&_mathId=si1.gif&_user=111111111&_pii=S0893965916302464&_rdoc=1&_issn=08939659&md5=88eb064d9c63bf29ff08a2889e4e382d" title="Click to view the MathML source">f(z,x)n>n class="mathContainer hidden">n class="mathCode">h id="mml1" overflow="scroll" altimg="si1.gif">f(z,x)h>n>n>n> with no growth restriction on the n id="mmlsi2" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302464&_mathId=si2.gif&_user=111111111&_pii=S0893965916302464&_rdoc=1&_issn=08939659&md5=026159a68209c0610870ee6ecdbd9e93" title="Click to view the MathML source">xn>n class="mathContainer hidden">n class="mathCode">h id="mml2" overflow="scroll" altimg="si2.gif">xh>n>n>n>-variable. We only assume that n id="mmlsi3" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302464&_mathId=si3.gif&_user=111111111&_pii=S0893965916302464&_rdoc=1&_issn=08939659&md5=471db93d58795b27573cbb5ef4798218" title="Click to view the MathML source">f(z,⋅)n>n class="mathContainer hidden">n class="mathCode">h id="mml3" overflow="scroll" altimg="si3.gif">f(z,⋅)h>n>n>n> is odd and superlinear near zero. Using a variant of the symmetric mountain pass theorem, we show that the problem has a whole sequence of distinct smooth nodal solutions converging to the trivial one.