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Quasilinear elliptic equations with critical growth involving jumping nonlinearities

机译：Quasilinear椭圆方程，涉及跳跃非线性的临界生长

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Abstract > In this paper we deal with the following class of quasilinear elliptic problems <displayedItem xml:id="mana201900099-disp-0001" type="mathematics" numbered="no"> <mat:math display="block" altimg="urn:x-wiley:0025584X:media:mana201900099:mana201900099-math-0001" wiley:location="equation/mana201900099-math-0001.png"> <mat:mrow> <mat:mspace width="81.0pt"/> <mat:mfenced separators="" open="{" close=""> <mat:mtable> <mat:mtr> <mat:mtd columnalign="right"> <mat:mrow> <mat:mo>?</mat:mo> <mat:msub> <mat:mi mathvariant="normal">Δ</mat:mi> <mat:mi>p</mat:mi> </mat:msub> <mat:mi>u</mat:mi> </mat:mrow> </mat:mtd> <mat:mtd> <mat:mo>=</mat:mo> </mat:mtd> <mat:mtd columnalign="left"> <mat:mrow> <mat:msup> <mat:mrow> <mat:mi>λ</mat:mi> <mat:mo stretchy="false">|</mat:mo> <mat:mi>u</mat:mi> <mat:mo stretchy="false">|</mat:mo> </mat:mrow> <mat:mrow> <mat:mi>p</mat:mi> <mat:mo>?</mat:mo> <mat:mn>2</mat:mn> </mat:mrow> </mat:msup> <mat:mi>u</mat:mi> <mat:mo>+</mat:mo> <mat:msubsup> <mat:mi>u</mat:mi> <mat:mo>+</mat:mo> <mat:mrow> <mat:msup> <mat:mi>p</mat:mi> <mat:mo>?</mat:mo> </mat:msup> <mat:mo>?</mat:mo> <mat:mn>1</mat:mn> </mat:mrow> </mat:msubsup> <mat:mo>+</mat:mo> <mat:mi>g</mat:mi> <mat:mo stretchy="true">(</mat:mo> <mat:mi>x</mat:mi> <mat:mo>,</mat:mo> <mat:msub> <mat:mi>u</mat:mi> <mat:mo>+</mat:mo> </mat:msub> <mat:mo stretchy="true">)</mat:mo> <mat:mo>+</mat:mo> <mat:mi>f</mat:mi> <mat:mrow> <mat:mo stretchy="false">(</mat:mo> <mat:mi>x</mat:mi> <mat:mo stretchy="false">)</mat:mo> </mat:mrow> <mat:mspace width="1em"/> <mat:mtext>in</mat:mtext> <mat:mspace width="1em"/> <mat:mi mathvariant="normal">Ω</mat:mi> <mat:mo>,</mat:mo> </mat:mrow> </mat:mtd> </mat:mtr> <mat:mtr> <mat:mtd columnalign="right"> <mat:mi>u</mat:mi> </mat:mtd> <mat:mtd> <mat:mo>=</mat:mo> </mat:mtd> <mat:mtd columnalign="left"> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> <div class="translation abstracttxt"> <span class="zhankaihshouqi fivelineshidden" id="abstract"> <span>机译：</span><Abstract Type =“Main”XML：Lang =“en”> <标题类型=“main”>抽象</ title> > 在本文中，我们应对以下类别的Quasilinear椭圆问题 <lightsitem xml：id =“mana201900099-disp-0001”类型=“数学”编号=“否” <mat：数学显示=“块”Altimg =“URN：X-Wiley：0025584X：MANA201900099：MANA201900099-MATH-0001”WIley：Location =“等式/ MANA201900099-MATH-0001.PNG”> <MAT：MROW> <mat：mspace width =“81.0pt”/> <mat：mfeced sectrators =“”打开=“{”close =“”> <mat：mtable> <MAT：MTR> <mat：mtd coloralalign =“右”> <MAT：MROW> <mat：mo>？</ mat：mo> <mat：msub> <mat：mi mathvariant =“正常”>δ</ mat：mi> <MAT：MI> P </ MAT：MI> </ mat：msub> <MAT：MI> U </ MAT：MI> </ mat：MROW> </ mat：mtd> <MAT：MTD> <mat：mo> = </ mat：mo> </ mat：mtd> <mat：mtd coloralalign =“left”> <MAT：MROW> <mat：msup> <MAT：MROW> <mat：mi>λ</ mat：mi> <MAT：MO弹力=“假”> | </ MAT：MO> <MAT：MI> U </ MAT：MI> <MAT：MO弹力=“假”> | </ MAT：MO> </ mat：MROW> <MAT：MROW> <MAT：MI> P </ MAT：MI> <mat：mo>？</ mat：mo> <MAT：MN> 2 </ MAT：MN> </ mat：MROW> </ mat：msup> <MAT：MI> U </ MAT：MI> <mat：mo> + </ mat：mo> <mat：msubsup> <MAT：MI> U </ MAT：MI> <mat：mo> + </ mat：mo> <MAT：MROW> <mat：msup> <MAT：MI> P </ MAT：MI> <mat：mo>？</ mat：mo> </ mat：msup> <mat：mo>？</ mat：mo> <MAT：MN> 1 </ MAT：MN> </ mat：MROW> </ mat：msubsup> <mat：mo> + </ mat：mo> <MAT：MI> G </ MAT：MI> <mat：mo stractry =“true”>（</ mat：mo> <mat：mi> x </ mat：mi> <mat：mo>，</ mat：mo> <mat：msub> <MAT：MI> U </ MAT：MI> <mat：mo> + </ mat：mo> </ mat：msub> <mat：mo stractry =“true”>）</ mat：mo> <mat：mo> + </ mat：mo> <MAT：MI> F </ MAT：MI> <MAT：MROW> <mat：mo stractry =“false”>（</ mat：mo> <mat：mi> x </ mat：mi> <mat：mo stractry =“假”>）</ mat：mo> </ mat：MROW> <mat：mspace width =“1em”/> <mat：mtext> </ mat：mtext> <mat：mspace width =“1em”/> <mat：mi mathvariant =“正常”>ω</ mat：mi> <mat：mo>，</ mat：mo> </ mat：MROW> </ mat：mtd> </ mat：MTR> <MAT：MTR> <mat：mtd coloralalign =“右”> <MAT：MI> U </ MAT：MI> </ mat：mtd> <MAT：MTD> <mat：mo> = </ mat：mo> </ mat：mtd> <mat：mtd coloralalign =“left”> </span> <span class="z_kbtn z_kbtnclass hoverxs" style="display: none;">展开▼</span> </div> </div> <div class="record"> <h2 class="all_title" id="enpatent33" >著录项</h2> <ul> <li> <span class="lefttit">来源</span> <div style="width: 86%;vertical-align: text-top;display: inline-block;"> <a href='/journal-foreign-24615/'>《Mathematische Nachrichten》</a> <b style="margin: 0 2px;">|</b><span>2020年第6期</span><b style="margin: 0 2px;">|</b><span>共16页</span> </div> </li> <li> <div class="author"> <span class="lefttit">作者</span> <p id="fAuthorthree" class="threelineshidden zhankaihshouqi"> </p> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zkzz" style="display: none;">展开▼</span> </div> </li> <li> <div style="display: flex;"> <span class="lefttit">作者单位</span> <div style="position: relative;margin-left: 3px;max-width: 639px;"> <div class="threelineshidden zhankaihshouqi" id="fOrgthree"> </div> <span class="z_kbtnclass z_kbtnclassall hoverxs" id="zhdw" style="display: none;">展开▼</span> </div> </div> </li> <li > <span class="lefttit">收录信息</span> <span style="width: 86%;vertical-align: text-top;display: inline-block;"></span> </li> <li> <span class="lefttit">原文格式</span> <span>PDF</span> </li> <li> <span class="lefttit">正文语种</span> <span>eng</span> </li> <li> <span class="lefttit">中图分类</span> <span><a href="https://www.zhangqiaokeyan.com/clc/156.html" title="数学">数学;</a></span> </li> <li class="antistop"> <span class="lefttit">关键词</span> <p style="width: 86%;vertical-align: text-top;"> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=Ambrosetti–Prodi type result&option=203" rel="nofollow">Ambrosetti–Prodi type result;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=critical Sobolev exponent&option=203" rel="nofollow">critical Sobolev exponent;</a> <a style="color: #3E7FEB;" href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=p ‐Laplace operator&option=203" rel="nofollow">p ‐Laplace operator;</a> </p> <div class="translation"> 机译：Ambrosetti-Prodi类型结果;关键的SoboLev指数;P -Laplace运算符; </div> </li> </ul> </div> </div> <div class="literature cardcommon"> <div class="similarity "> <h3 class="all_title" id="enpatent66">相似文献</h3> <div class="similaritytab clearfix"> <ul> <li class="active" >外文文献</li> <li >中文文献</li> <li >专利</li> </ul> </div> <div class="similarity_details"> <ul > <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/journal-foreign-detail/0704023595684.html">Quasilinear elliptic equations with critical growth involving jumping nonlinearities</a> <b>[J]</b> . <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> </a> <a href="/journal-foreign-24615/" target="_blank" rel="nofollow" class="tuijian_authcolor">Mathematische Nachrichten .</a> <span>2020</span><span>,第6期</span> </span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: 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href="/academic-conference-cn_meeting-22804_thesis/02022715804.html">横向排列双圆柱绕流的临界Re数和St数跳跃</a> <b>[C]</b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘坤&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 刘坤</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=马东军&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,马东军</a> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=孙德军&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor">,孙德军</a> <span> <a href="/conference-cn-22804/" target="_blank" rel="nofollow" class="tuijian_authcolor"> . 第十一届全国分离流、旋涡和流动控制会议 </a> <span> <span> . 2006</span> </span> </div> </li> <li> <div> <b>7. </b><a class="enjiyixqcontent" href="/academic-degree-domestic_mphd_thesis/020315836866.html">含凹及临界非线性项的半线性椭圆方程的多解问题</a> <b>[A] </b> <span> <a href="/search.html?doctypes=4_5_6_1-0_4-0_1_2_3_7_9&sertext=刘美淇&option=202" target="_blank" rel="nofollow" class="tuijian_auth tuijian_authcolor"> . 刘美淇</a> <span> . 2020</span> </span> </div> </li> </ul> <ul style="display: none;"> <li> <div> <b>1. </b><a class="enjiyixqcontent" href="/patent-detail/06120105060793.html">使用非线性光学技术检测涉及构象变化的相互作用的方法</a> <b>[P]</b> . <span> 中国专利： CN1864066A </span> <span> . 2006-11-15</span> </div> </li> <li> <div> <b>2. </b><a class="enjiyixqcontent" href="/patent-detail/06120784489.html">涉及临界资源的中断处理方法和装置及实时操作系统</a> <b>[P]</b> . <span> 中国专利： CN101482833B </span> <span> . 2011.06.15</span> </div> </li> <li> <div> <b>3. </b><a class="enjiyixqcontent" href="/patent-detail/06130419135041.html">Method for computer-aided generation of cryptographic data by e.g. smart card based on elliptic curve, involves transforming projective representations of x-coordinate of point of curve to other representations by preset equations</a> <b>[P]</b> . <span> 外国专利：  DE102012210354B3 </span> <span> . 2013-11-07</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：通过例如计算机辅助生成密码数据的方法基于椭圆曲线的智能卡，涉及通过预设方程将曲线点的x坐标的投影表示转换为其他表示 </span> </p> </li> <li> <div> <b>4. </b><a class="enjiyixqcontent" href="/patent-detail/06130441255052.html">Data encryption method for, e.g., chip card, involves using hyper elliptical curves of genus 2 having specified equation that satisfies specified conditions</a> <b>[P]</b> . <span> 外国专利：  FR2852470A1 </span> <span> . 2004-09-17</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：用于例如芯片卡的数据加密方法涉及使用具有满足指定条件的指定方程的第二类超椭圆曲线 </span> </p> </li> <li> <div> <b>5. </b><a class="enjiyixqcontent" href="/patent-detail/06130500596681.html">Voltage and current characteristics of LEDsThe experimental equation of the best matching equation is calculated by solving the nonlinear equation, which is not a binary coalition or coalition, using the method of least squares method, by solving the Newton method to the computer.Using the expressionA method of obtaining a current value when a value of resistance is specified in a circuit comprising only one LED and one resistor and a DC power supply, as well as finding a forward voltage drop when a certain current flows</a> <b>[P]</b> . <span> 外国专利：  JP2021132237A </span> <span> . 2021-09-09</span> </div> <p class="zwjiyix translation" style="max-width: initial;height: auto;word-break: break-all;white-space: initial;text-overflow: initial;overflow: initial;"> <span>机译：通过求解非线性联盟或联盟的非线性方程来计算最佳匹配方程的LEDSTHE实验方程的电压和电流特性，这不是二进制联盟或联盟的方法，通过求解牛顿方法到计算机。使用表达式当在仅包括一个LED和一个电阻器和DC电源的电路中指定电阻值时获得电流值的方法，以及当某个电流流动时找到正向电压降 </span> </p> </li> </ul> </div> </div> </div> <div class="theme cardcommon" style="overflow: auto;display:none"> <h3 class="all_title" id="enpatent55">相关主题</h3> <ul id="subject"> </ul> </div> </div> </div> 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