Periodic solutions for discontinuous perturbations of the relativistic operator

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• 作者：Petru Jebelean^a ; ^b ; ^{jebelean@math.uvt.ro" class="auth_mail" title="E-mail the corresponding author} ; Jean Mawhin^c ; ^{jean.mawhin@uclouvain.be" class="auth_mail" title="E-mail the corresponding author} ; Călin Şerban^a ; ^{cserban2005@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34A60 ; 47H14 ; 49J52 ; 49K21
• 刊名：Bulletin des Sciences Mathematiques
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：140
• 期：1
• 页码：99-117
• 全文大小：365 K

文摘

In this paper we study the existence and multiplicity of periodic solutions for discontinuous perturbations of the operator class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S000744971500010X&_mathId=si1.gif&_user=111111111&_pii=S000744971500010X&_rdoc=1&_issn=00074497&md5=eb70c29f6a78e802b465ec77484d8d10">class="imgLazyJSB inlineImage" height="32" width="117" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S000744971500010X-si1.gif">class="mathContainer hidden">class="mathCode">$u\mapsto {\left(\frac{u^{\prime }}{\sqrt{1-{|u^{\prime }|}^2}}\right)}^{\prime }$. The results are obtained by reduction to an equivalent non-singular problem and using the non-smooth critical point theory. Some illustrative examples concerning Filippov type solutions are also provided.