Publication Cover
Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 4
147
Views
3
CrossRef citations to date
0
Altmetric
Articles

On the eigenvalues and Fučik spectrum of p-fractional Hardy-Sobolev operator with weight function

Pages 633-658 | Received 17 Aug 2016, Accepted 09 Jan 2017, Published online: 23 Jan 2017

References

  • Frank RL, Seiringer R. Non-linear ground state representations and sharp Hardy inequlities. J Funct Anal. 2008;255:3407–3430.
  • Adimurthi. Hardy--Sobolev inequality in H1(Ω) and its applications. Commun Contemp Math. 2002;3:409–434.
  • Adimurthi, Sandeep K. Existence and non-existence of the first eigenvalue of the perturbed Hardy--Sobolev operator. Proc R Soc Edinburgh Sect A. 2002;132(5):1021–1043.
  • Sandeep K, Sreenadh K. Asymptotic behaviour of the rst eigenfunction of a perturbed Hardy--Sobolev operator. Nonlinear Anal Theory Methods Appl. 2003;53(3):545–563.
  • Sreenadh K. On the second eigenvalue of a Hardy--Sobolev operator. Elect J Differ Equ. 2004;2004(12):1–9.
  • Sreenadh K. On the Fučik spectrum of Hardy Sobolev operator. Nonlinear Anal Theory Methods Appl. 2002;51:1167–1185.
  • Sreenadh K. On the eigenvalue problem for the Hardy--Sobolev operator with indefinite weights. Elect J Differ Equ. 2002;33:1–12.
  • Dancer EN. On the Dirichlet problem for weakly non-linear elliptic partial differential equations. Proc R Soc Edinburgh Sect A. 1976/1977;76(4):283–300.
  • Alif M. Fučik spectrum for the Neumann problem with indefinite weights, Partial differential equations. Vol. 229. Lecture notes in pure and Applied Mathematics. New York (NY): Dekker; 2002. p. 45–62.
  • Cuesta M, de Figueiredo D, Gossez J-P. The beginning of the Fučik spectrum for the p-Laplacian. J Differ Equ. 1999;159:212–238.
  • Cuesta M, Gossez J-P. A variational approach to nonresonance with respect to the Fučik spectrum. Nonlinear Anal. 1992;19:487–500.
  • de Figueiredo D, Gossez J-P. On the first curve of the Fučik spectrum of an elliptic operator. Differ. Integral Equ. 1994;7:1285–1302.
  • Motreanu Dumitru, Winkert Patrick. On the Fučik spectrum of p-Laplacian with Robin boundary condition. Nonlinear Anal. 2011;74:4671–4681.
  • Martinez SR, Rossi JD. On the Fučik spectrum and a resonance problem for the p-Laplacian with a nonlinear boundary condition. Nonlinear Anal Theory Methods Appl. 2004;59(6):813–848.
  • Perera K. On the Fučik spectrum of the p-Laplacian. Nonlinear Differ Equ Appl. 2004;11(2):259–270.
  • Perera K. Resonance problems with respect to the Fučik spectrum of the p-Laplacian. Elect J Differ Equ. 2002;2002:1–10.
  • Cuesta M. Eigenvalue problem for the p–Laplacian with indefinite weights. Electron J Differ Equ. 2001;2001:1–33.
  • Bisci GM, Radulescu VD, Servadei R. Variational methods for nonlocal fractional problems. Vol. 162, Encyclopedia of mathematics and its applications. Cambridge: Cambridge University Press; 2016.
  • Ferrara M, Bisci GM. Existence results for elliptic problems with Hardy potential. Bull Sci Math. 2014;138(7):846–859.
  • Goyal S, Sreenadh K. Existence of multiple solutions of p-fractional Laplace operator with sign-changing weight function. Adv Nonlinear Anal. 2015;4(1):37–58.
  • Goyal S, Sreenadh K. The Nehari manifold for non-local elliptic operator with concave-convex nonlinearities and sign-changing weight functions. Proc Indian Acad Math Sci. 2015;125(4):545–558.
  • Servadei R, Valdinoci E. Variational methods for non-local operators of elliptic type, Discrete Contin Dyn Syst. 2013;33(5):2105–2137.
  • Lindgren E, Lindqvist P. Fractional eigenvalues. Calc Var Partial Differ Equ. 2013;49:795–826.
  • Franzina G, Palatucci G. Fractional p-eigenvalues. Riv Mat Univ Parma. 2014;5(2):373–386.
  • Iannizzotto A, Squassina M. Weyl-type laws for fractional p-eigenvalue problems. Asymptot Anal. 2014;88(1):233–245.
  • Brasco L, Parini E, Squassina M. Stability of variational eigenvalues for the fractional p-Laplacian. Discrete Contin Dyn Syst A. 2016;36:1813–1845.
  • Pezzo LD, Bonder JF, Rios LL. An optimization problem for the first eigenvalue of the p-fractional Laplacian. arXiv:1601.03019 [math.AP].
  • Del Pezzo LM, Quaas A. Global bifurcation for fractional p-Laplacian and application. Z Anal Anwend. 2016;35:411–447.
  • Goyal S, Sreenadh K. On the Fučik spectrum of non-local elliptic operators. Nonlinear Differ Equ Appl. 2014;21:567–588.
  • Perera K, Squassina M, Yang Y. A note on the Dancer-Fučik spectra of the fractional p-Laplacian and Laplacian operators. Adv Nonlinear Anal. 2015;8:13–23.
  • Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 2012;136:225–236.
  • Servadei R, Valdinoci E. Mountain pass solutions for non-local elliptic operators. J Math Anal Appl. 2012;389:887–898.
  • Amghibech S. On the discrete version of Picone’s identity. Discrete App Math. 2008;156(1):1–10.
  • Brezis H, Lieb E. A relation between point convergence of functions and convergence of functionals. Proc Am Math Soc. 1983;88:486–490.
  • Struwe M. Variational methods. New York (NY): Springer; 2000.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.