Asymmetric (p, 2)-equations with double resonance View Full Text


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Article Info

DATE

2017-06-03

AUTHORS

Leszek Gasiński, Nikolaos S. Papageorgiou

ABSTRACT

We consider a nonlinear Dirichlet elliptic problem driven by the sum of a p-Laplacian and a Laplacian [a (p, 2)-equation] and with a reaction term, which is superlinear in the positive direction (without satisfying the Ambrosetti–Rabinowitz condition) and sublinear resonant in the negative direction. Resonance can also occur asymptotically at zero. So, we have a double resonance situation. Using variational methods based on the critical point theory and Morse theory (critical groups), we establish the existence of at least three nontrivial smooth solutions. More... »

PAGES

88

References to SciGraph publications

  • 2013-11-05. Qualitative Phenomena for Some Classes of Quasilinear Elliptic Equations with Multiple Resonance in APPLIED MATHEMATICS & OPTIMIZATION
  • 2000-10. Solitons in Several Space Dimensions:¶Derrick's Problem and¶Infinitely Many Solutions in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1993. Infinite Dimensional Morse Theory and Multiple Solution Problems in NONE
  • 2011-10-18. Multiple Solutions for Nonlinear Coercive Problems with a Nonhomogeneous Differential Operator and a Nonsmooth Potential in SET-VALUED AND VARIATIONAL ANALYSIS
  • 2014. Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems in NONE
  • 2012-12-28. Multiplicity of positive solutions for eigenvalue problems of (p,2)-equations in BOUNDARY VALUE PROBLEMS
  • 2003-07. On a resonant-superlinear elliptic problem in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2002-06. Homotopical Stability of Isolated Critical Points of Continuous Functionals in SET-VALUED AND VARIATIONAL ANALYSIS
  • 1995-05. Nontrivial solutions for a Neumann problem with a nonlinear term asymptotically linear at −∞ and superlinear at +∞ in MATHEMATISCHE ZEITSCHRIFT
  • 2007. The Maximum Principle in NONE
  • 2011-07-26. Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), no. 3, 379-391, and a comment on the generalized Ambrosetti-Rabinowitz condition in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
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    http://scigraph.springernature.com/pub.10.1007/s00526-017-1180-2

    DOI

    http://dx.doi.org/10.1007/s00526-017-1180-2

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