Multiplicity results for the Kirchhoff type equations with critical growth

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• 作者：Liu Yangp>ap> ; Zhisu Liup>bp>p> ; p>p>liuzhisu183@sina.com" class="auth_mail" title="E-mail the corresponding authorp> ; Zigen Ouyangp>bp>
• 关键词：Multiplicity ; Kirchhoff type equation ; Critical growth
• 刊名：Applied Mathematics Letters
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：63
• 期：Complete
• 页码：118-123
• 全文大小：590 K

文摘

In this paper, we study the following Kirchhoff type equation with critical growth where pan id="mmlsi2" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si2.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=33fb950e2aefa5dbfdb99496994fc062" title="Click to view the MathML source">a>0,b≥0pan>pan class="mathContainer hidden">pan class="mathCode">$a>0,\mathrm{<font\; color="red">b</font>}\ge 0$pan>pan>pan> and pan id="mmlsi3" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si3.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=398727f33b6213eb3973e75ca1685996" title="Click to view the MathML source">Ωpan>pan class="mathContainer hidden">pan class="mathCode">$\Omega$pan>pan>pan> is a smooth bounded domain in pan id="mmlsi4" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si4.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=ebd42ef49dd29d2195a05563abeb98a9" title="Click to view the MathML source">Rp>3p>pan>pan class="mathContainer hidden">pan class="mathCode">pan>pan>pan>. When the real parameter pan id="mmlsi5" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si5.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=cc0e9ea79a02c1bc6e6fa900b1777f5f" title="Click to view the MathML source">μpan>pan class="mathContainer hidden">pan class="mathCode">$\mu$pan>pan>pan> is larger than some positive constant, we investigate the multiplicity of nontrivial solutions for the above problem with parameter pan id="mmlsi6" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si6.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=f67cf5f117fda276f3542cb282631913" title="Click to view the MathML source">λpan>pan class="mathContainer hidden">pan class="mathCode">$\lambda$pan>pan>pan> belonging to a left neighborhood of the Dirichlet eigenvalue of the Laplacian operator pan id="mmlsi7" class="mathmlsrc">pan class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0893965916302233&_mathId=si7.gif&_user=111111111&_pii=S0893965916302233&_rdoc=1&_issn=08939659&md5=338b67f8abe230159956e416aba2ebef" title="Click to view the MathML source">−△pan>pan class="mathContainer hidden">pan class="mathCode">$-△$pan>pan>pan>.