Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{am ...

p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts}... We prove existence, multiplicity, and bifurcation results for p-Laplacian problems involving critical Hardy–Sobolev exponents. Our results are mainly for the case λ≥λ1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda \ge \lambda _1$$\end{document} and extend results in the literature for 0<λ<λ1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0< \lambda < \lambda _1$$\end{document}. In the absence of a direct sum decomposition, we use critical point theorems based on a cohomological index and a related pseudo-index. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Nonlinear Differential Equations and Applications NoDEA Springer Journals

p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{am ...

Download PDF
16 pages

Loading next page...
 
/lp/springer_journal/varvec-p-p-laplacian-problems-involving-critical-hardy-sobolev-UKG1XSAFwr
Publisher
Springer Journals
Copyright
Copyright © Springer International Publishing AG, part of Springer Nature 2018
Subject
Mathematics; Analysis
ISSN
1021-9722
eISSN
1420-9004
DOI
10.1007/s00030-018-0517-7
Publisher site
See Article on Publisher Site

Abstract

We prove existence, multiplicity, and bifurcation results for p-Laplacian problems involving critical Hardy–Sobolev exponents. Our results are mainly for the case λ≥λ1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\lambda \ge \lambda _1$$\end{document} and extend results in the literature for 0<λ<λ1\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$0< \lambda < \lambda _1$$\end{document}. In the absence of a direct sum decomposition, we use critical point theorems based on a cohomological index and a related pseudo-index.

Journal

Nonlinear Differential Equations and Applications NoDEA – Springer Journals

Published: Jun 1, 2018

Keywords: p-Laplacian problems; Critical Hardy–Sobolev exponents; Existence; Multiplicity; Bifurcation; Critical point theory; Cohomological index; Pseudo-index; Primary 35J92; 35B33; Secondary 35J20

References

  • Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
    Bartolo, P; Benci, V; Fortunato, D
  • On critical point theory for indefinite functionals in the presence of symmetries
    Benci, Vieri
  • Linking over cones and nontrivial solutions for p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Laplace equations with p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-superlinear nonlinearity
    Degiovanni, Marco; Lancelotti, Sergio
  • Linking solutions for p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Laplace equations with nonlinearity at critical growth
    Degiovanni, Marco; Lancelotti, Sergio
  • Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
    Fadell, Edward R; Rabinowitz, Paul H
  • Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents
    Ghoussoub, N; Yuan, C
  • The Brezis–Nirenberg problem for the fractional p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Laplacian
    Mosconi, S; Perera, K; Squassina, M; Yang, Y
  • Nontrivial critical groups in p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Laplacian problems via the Yang index
    Perera, Kanishka
  • Bifurcation and multiplicity results for critical p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Laplacian problems
    Perera, Kanishka; Squassina, Marco; Yang, Yang
  • p\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p$$\end{document}-Laplacian problems where the nonlinearity crosses an eigenvalue
    Perera, Kanishka; Szulkin, Andrzej
  • Some critical point theorems and applications to semilinear elliptic partial differential equations
    Rabinowitz, Paul H
  • N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N$$\end{document}-Laplacian problems with critical Trudinger-Moser nonlinearities
    Yang, Yang; Perera, Kanishka