where Δpu=div(|∇u|p−2∇u) is the p-Laplacian operator, Ω⫅ℝN is a bounded domain with smooth boundary, h and g are bounded functions, N≥1 and 1<p<∞. Using the Mountain Pass Theorem and the Ekeland Variational Principle, we will show the existence of at least three solutions for (P).">
涉及p-拉普拉斯共振的问题的多重解</gydF4y2Batitle>
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<a class="sc-htpNat bUhGXt link sc-nrwXf kCVAWK breadCrumb" href="//www.newsama.com/journals/aaa/" aria-label="Abstract and Applied Analysis">抽象与应用分析</gydF4y2Baa>/<gydF4y2Baa class="sc-htpNat bUhGXt link sc-nrwXf kCVAWK breadCrumb" href="//www.newsama.com/journals/aaa/contents/year/1998/" aria-label="1998">1998</gydF4y2Baa>/<gydF4y2Baspan class="sc-eitiEO cWbOKB">文章</gydF4y2Baspan>
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<p>在这一页上</pgydF4y2Ba>
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<p class="sc-gmeYpB ctdkmR article_type">开放获取</pgydF4y2Ba>
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体积<gydF4y2Ba!-- -->
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<span class="sc-iSDuPN ezntTT">|</gydF4y2Baspan>
<a class="sc-htpNat bUhGXt link sc-fZwumE dqIsrA" href="https://doi.org/10.1155/S1085337598000517" aria-label="Doi-link">https://doi.org/10.1155/S1085337598000517</gydF4y2Baa>
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<p>C. O. Alves, P. C. Carrião, O. H.宫崎<gydF4y2Ba!-- -->，<gydF4y2Ba!-- -->
<!-- -->＂<gydF4y2Baspan class="adjust-article-svg-size">一个问题的多个解决方案与共振涉及<gydF4y2Bamml:math alttext="$p$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
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</mml:math>拉普拉斯算子</gydF4y2Baspan>"，<gydF4y2Ba!-- --><i>抽象与应用分析</gydF4y2Bai>，<gydF4y2Ba!-- -->
<!-- -->卷。<gydF4y2Ba!-- -->3.<gydF4y2Ba!-- -->，<gydF4y2Ba!-- -->
<!-- -->文章的ID<gydF4y2Ba!-- -->315492<gydF4y2Ba!-- -->，<gydF4y2Ba!-- -->
<!-- -->11<gydF4y2Ba!-- -->
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<!-- -->页面<gydF4y2Ba!-- -->，<gydF4y2Ba!-- -->
<!-- -->1998<gydF4y2Ba!-- -->．<gydF4y2Ba!-- -->
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<h1 class="sc-iRbamj jZOxOO sc-RcBXQ goubQH article_title adjust-article-svg-size heading-title">一个问题的多个解决方案与共振涉及<gydF4y2Bamml:math alttext="$p$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
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<div class="sc-gPzReC fMlAsT article_authors">
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<span class="">c·o·阿尔维斯<gydF4y2Ba!-- -->，<gydF4y2Basup>1</gydF4y2Basup></span>
<span class="">p c Carriao<gydF4y2Ba!-- -->，<gydF4y2Basup>2</gydF4y2Basup>
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<span class="">o . h . Miyagaki<gydF4y2Basup>3.</gydF4y2Basup></span>
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<p><sup>1</gydF4y2Basup><span>巴西联邦大学Paraíba省matemática e Estatística</gydF4y2Baspan></p>
<p><sup>2</gydF4y2Basup><span>巴西米纳斯吉拉斯州联邦大学Matemática学院</gydF4y2Baspan></p>
<p><sup>3.</gydF4y2Basup><span>巴西联邦大学Matemática</gydF4y2Baspan></p>
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<div class="articleContent__PublcationCol-sc-2yl9jy-5 hgKieC notPublished">
<span class="articleContent__PublicationField-sc-2yl9jy-6 cIribm">收到了</gydF4y2Baspan>
<span class="articleContent__PublicationValue-sc-2yl9jy-7 khHUcu">1998年3月18日</gydF4y2Baspan>
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<h4 class="header" id="abstract">摘要</hgydF4y2Ba4>
<p>本文将研究该问题的多解的存在性<gydF4y2Bamml:math display="block" alttext="$-\Delta_pu + g(x,u) =\lambda_1h(x)|u|^{p-2}u,\mathrm{in}\Omega,u\in H_0^{1,p}(\Omega)(P)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
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<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mo>
−</gydF4y2Bamml:mo>
<mml:msub>
<mml:mi>
Δ</gydF4y2Bamml:mi>
<mml:mi>
p</gydF4y2Bamml:mi>
</mml:msub>
<mml:mi>
u</gydF4y2Bamml:mi>
<mml:mo>
+</gydF4y2Bamml:mo>
<mml:mi>
g</gydF4y2Bamml:mi>
<mml:mrow>
<mml:mo>
（</gydF4y2Bamml:mo>
<mml:mrow>
<mml:mi>
x</gydF4y2Bamml:mi>
<mml:mo>
，</gydF4y2Bamml:mo>
<mml:mi>
u</gydF4y2Bamml:mi>
</mml:mrow>
<mml:mo>
）</gydF4y2Bamml:mo>
</mml:mrow>
<mml:mo>
＝</gydF4y2Bamml:mo>
<mml:msub>
<mml:mi>
λ</gydF4y2Bamml:mi>
<mml:mn>
1</gydF4y2Bamml:mn>
</mml:msub>
<mml:mi>
h</gydF4y2Bamml:mi>
<mml:mrow>
<mml:mo>
（</gydF4y2Bamml:mo>
<mml:mi>
x</gydF4y2Bamml:mi>
<mml:mo>
）</gydF4y2Bamml:mo>
</mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
|</gydF4y2Bamml:mo>
<mml:mi>
u</gydF4y2Bamml:mi>
<mml:mo>
|</gydF4y2Bamml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>
p</gydF4y2Bamml:mi>
<mml:mo>
−</gydF4y2Bamml:mo>
<mml:mn>
2</gydF4y2Bamml:mn>
</mml:mrow>
</mml:msup>
<mml:mi>
u</gydF4y2Bamml:mi>
<mml:mo>
，</gydF4y2Bamml:mo>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
在</gydF4y2Bamml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mi>
Ω</gydF4y2Bamml:mi>
<mml:mo>
，</gydF4y2Bamml:mo>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mtext>
</mml:mtext>
<mml:mi>
u</gydF4y2Bamml:mi>
<mml:mo>
∈</gydF4y2Bamml:mo>
<mml:msubsup>
<mml:mi>
H</gydF4y2Bamml:mi>
<mml:mn>
0</gydF4y2Bamml:mn>
<mml:mrow>
<mml:mn>
1</gydF4y2Bamml:mn>
<mml:mo>
，</gydF4y2Bamml:mo>
<mml:mi>
p</gydF4y2Bamml:mi>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo>
（</gydF4y2Bamml:mo>
<mml:mi>
Ω</gydF4y2Bamml:mi>
<mml:mo>
）</gydF4y2Bamml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>在哪里<gydF4y2Bamml:math alttext="$\Delta_{p}u =\mathrm{div}(|\nabla u|^{p-2}\nabla u)$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:msub>
<mml:mi>
Δ</gydF4y2Bamml:mi>
<mml:mi>
p</gydF4y2Bamml:mi>
</mml:msub>
<mml:mi>
u</gydF4y2Bamml:mi>
<mml:mo>
＝</gydF4y2Bamml:mo>
<mml:mtext>
div</gydF4y2Bamml:mtext>
<mml:mrow>
<mml:mo>
（</gydF4y2Bamml:mo>
<mml:mrow>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo>
|</gydF4y2Bamml:mo>
<mml:mrow>
<mml:mo>
∇</gydF4y2Bamml:mo>
<mml:mi>
u</gydF4y2Bamml:mi>
</mml:mrow>
<mml:mo>
|</gydF4y2Bamml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mi>
p</gydF4y2Bamml:mi>
<mml:mo>
−</gydF4y2Bamml:mo>
<mml:mn>
2</gydF4y2Bamml:mn>
</mml:mrow>
</mml:msup>
<mml:mo>
∇</gydF4y2Bamml:mo>
<mml:mi>
u</gydF4y2Bamml:mi>
</mml:mrow>
<mml:mo>
）</gydF4y2Bamml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>是<gydF4y2Bamml:math alttext="$p$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>
p</gydF4y2Bamml:mi>
</mml:math>拉普拉斯算符,<gydF4y2Bamml:math alttext="$\Omega\subseteq\mathbb{R}^N$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
Ω</gydF4y2Bamml:mi>
<mml:mo>
⫅</gydF4y2Bamml:mo>
<mml:msup>
<mml:mi>
ℝ</gydF4y2Bamml:mi>
<mml:mi>
N</gydF4y2Bamml:mi>
</mml:msup>
</mml:mrow>
</mml:math>是一个边界光滑的有界域，<gydF4y2Bamml:math alttext="$h$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>
h</gydF4y2Bamml:mi>
</mml:math>和<gydF4y2Bamml:math alttext="$g$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mi>
g</gydF4y2Bamml:mi>
</mml:math>是有界函数,<gydF4y2Bamml:math alttext="$N\geq 1$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mi>
N</gydF4y2Bamml:mi>
<mml:mo>
≥</gydF4y2Bamml:mo>
<mml:mn>
1</gydF4y2Bamml:mn>
</mml:mrow>
</mml:math>和<gydF4y2Bamml:math alttext="$1 < p < \infty$" xmlns:mml="http://www.w3.org/1998/Math/MathML">
<mml:mrow>
<mml:mn>
1</gydF4y2Bamml:mn>
<mml:mo>
<</gydF4y2Bamml:mo>
<mml:mi>
p</gydF4y2Bamml:mi>
<mml:mo>
<</gydF4y2Bamml:mo>
<mml:mi>
∞</gydF4y2Bamml:mi>
</mml:mrow>
</mml:math>．利用山口定理和Ekeland变分原理，我们将证明(P)的至少三个解的存在性。</pgydF4y2Ba>
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<h4 class="copyright" id="copyright">版权</hgydF4y2Ba4>
<p>Hindawi出版公司版权所有这是一篇开放获取的文章<gydF4y2Baa rel="license" href="http://creativecommons.org/licenses/by/3.0/">知识共享署名许可</gydF4y2Baa>，允许在任何媒介上不受限制地使用、分发和复制，只要原稿被适当引用。</pgydF4y2Ba>
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<a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-cBdUnI bmjKRX pdf_desktop button__group" href="https://downloads.hindawi.com/journals/aaa/1998/315492.pdf" aria-label="" target="_blank" id="toolbar__dcNavSmall"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="https://static-01.hindawi.com/next_assets/d1LIQ_2PXn-51qq_Oxf54/_next/static/node_modules/hindawi-ui/src/icon/svg/pdf.svg" height="24"><span class="text">PDF</gydF4y2Baspan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a>
<a class="sc-htpNat bUhGXt link sc-jtRfpW dIjoCg sc-exkUMo huSjso ref_desktop" href="//www.newsama.com/journals/aaa/1998/315492.ris" aria-label="" target="" id="toolbar__dcNavLarge"><span><img alt="" class="sc-EHOje jOLhQl sc-kTUwUJ eujois" title="" role="presentation" src="data:image/svg+xml;base64,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" height="24"><span class="text">下载引用</gydF4y2Baspan></span><span class="sc-htoDjs bqeMOy sc-dqBHgY cQgXqt fileArrow icon-colored _3P4iUn1NDM5G77nWCamJ4l icon-themeable" title="" font-size="20"></span></a>
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的观点<gydF4y2Baspan>155</gydF4y2Baspan>
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下载<gydF4y2Baspan>553</gydF4y2Baspan>
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