Critical Points for a Functional Involving Critical Growth of Trudinger–Moser Type

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• 作者：Jo?o Marcos do ó ; Manassés de Souza ; Everaldo de Medeiros…
• 关键词：Critical points ; Least energy ; Concentration ; compactness principle ; Trudinger–Moser inequality ; 35J60 ; 35J20 ; 35B33
• 刊名：Potential Analysis
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：42
• 期：1
• 页码：229-246
• 全文大小：377 KB
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  3. Adimurthi, Yang, Y.: An interpolation of hardy inequality and Trudinger–moser inequality in ?sup class="a-plus-plus"> / n and its applications. Int. Math. Res. Not. IMRN, 2394-426 (2010)
  4. Berestycki, H., Lions, P.-L.: Nonlinear scalar field equations I. Existence of a ground state. Arch. Rational Mech. Anal. 82, 313-45 (1983)
  5. Cao, D. M.: Nontrivial solution of semilinear elliptic equation with critical exponent in ?sup class="a-plus-plus">2. Comm. Partial Differ. Equ. 17, 407-35 (1992) doi.org/10.1080/03605309208820848" target="_blank" title="It opens in new window">CrossRef
  6. ?erny, R., Cianchi, A., Hencl, S.: Concentration-compactness principles for Moser-Trudinger inequalities: new results and proofs. Annali di Matematica Pura ed Applicata 192, 225-43 (2013) doi.org/10.1007/s10231-011-0220-3" target="_blank" title="It opens in new window">CrossRef
  7. de Figueiredo, D.G., do ó, J.M., Ruf, B.: Elliptic equations and systems with critical Trudinger-moser nonlinearities. Discret. Contin. Dyn. Syst. 30, 455-76 (2011) doi.org/10.3934/dcds.2011.30.455" target="_blank" title="It opens in new window">CrossRef
  8. de Figueiredo, D.G., Miyagaki, O.H., Ruf, B.: Elliptic equations in ?sup class="a-plus-plus">2 with nonlinearities in the critical growth range. Calc. Var Partial Differ. Equ. 4, 139-53 (1995) doi.org/10.1007/BF01205003" target="_blank" title="It opens in new window">CrossRef
  9. de Morais Filho, D.C., Souto, M.A.S., do ó, J.M.: A compactness embedding lemma, a principle of symmetric criticality and applications to elliptic problems. Proyecciones. 19, 1-7 (2000) doi.org/10.4067/S0716-09172000000100001" target="_blank" title="It opens in new window">CrossRef
  10. de Souza, M.: On a singular elliptic problem involving critical growth in ?sup class="a-plus-plus"> / n . NoDEA Nonlinear Differ. Equ. Appl. 18, 199-15 (2011) doi.org/10.1007/s00030-010-0091-0" target="_blank" title="It opens in new window">CrossRef
  11. de Souza, M., do ó, J.M.: On singular Trudinger-moser type inequalities for unbounded domains and their best exponents. Potential Analysis 38, 1091-101 (2013) doi.org/10.1007/s11118-012-9308-7" target="_blank" title="It opens in new window">CrossRef
  12. de Souza, M., do ó, J.M.: On a class of singular Trudinger-Moser type inequalities and its applications. Math. Nachr. 284, 1754-776 (2011) doi.org/10.1002/mana.201000083" target="_blank" title="It opens in new window">CrossRef
  13. do ó, J.M.: Semilinear Dirichlet problems for the / n?Laplacian in ?sup class="a-plus-plus"> / n with nonlinearities in critical growth range. Differ. Integr. Equ. 9, 967-79 (1996)
  14. do ó, J.M.: / n-Laplacian equations in ?sup class="a-plus-plus"> / n with critical growth. Abstr. Appl. Anal. 2, 301-15 (1997) doi.org/10.1155/S1085337597000419" target="_blank" title="It opens in new window">CrossRef
  15. do ó, J.M., Medeiros, E., Severo, U.B.: A nonhomogeneous elliptic problem involving critical growth in dimension two. J. Math. Anal. Appl. 345, 286-04 (2008) doi.org/10.1016/j.jmaa.2008.03.074" target="_blank" title="It opens in new window">CrossRef
  16. do ó, J.M., Medeiros, E., Severo, U.B.: On a quasilinear nonhomogeneous elliptic equation with critical growth in ?sup class="a-plus-plus"> / n . J. Diff. Equat. 246, 1363-386 (2009) doi.org/10.1016/j.jde.2008.11.020" target="_blank" title="It opens in new window">CrossRef
  17. Díaz, J.I.: Nonlinear partia
• 作者单位：Jo?o Marcos do ó (1)
  Manassés de Souza (1)
  Everaldo de Medeiros (1)
  Uberlandio Severo (1)
  
  1. Departamento de Matemática, Universidade Federal da Paraíba, 58051-900, Jo?o Pessoa, PB, Brazil
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Potential Theory
  Probability Theory and Stochastic Processes
  Geometry
  Functional Analysis
  
• 出版者：Springer Netherlands
• ISSN：1572-929X

文摘

We establish the existence of critical points of leat energy for functionals associated with a class of singular quasilinear elliptic equations involving critical growth of Trudinger-Moser type. For this, in line with the Concentration-a href='/search?dc.title=Compactness&facet-content-type=ReferenceWorkEntry&sortOrder=relevance' class='reference-link webtrekk-track' gaCategory="Internal link" gaLabel="Compactness" gaAction="reference keyword">Compactness Principle due to P. -L. Lions (I. Rev. Mat. Iberoamericana 1, 145-01, 1985), we study the lack of compactness of Sobolev imbedding in Orlicz space defined in ?sup class="a-plus-plus"> n (n ?2).