Multiplicity of solutions for fractional p-Laplacian equation with indefinite nonlinearity

References

• Andreu F, Mazón JM, Rossi JD, et al. Nonlocal diffusion problems. Providence (RI): AMS; 2010. (Mathematical surveys and monographs; 165).
   Google Scholar
• Brasco L, Parini E. The second eigenvalue of the fractional p-Laplacian. Adv Calc Var. 2016;9:323–355.
   Web of Science ®Google Scholar
• Franzina G, Palatucci G. Fractional p-eigenvalues. Riv Mat Univ Parma. 2014;5:315–328.
   Google Scholar
• Lindgren E, Lindqvist P. Fractional eigenvalues. Calc Var Partial Differ Equ. 2014;49:795–826.
   Web of Science ®Google Scholar
• Di Castro A, Kuusi T, Palatucci G. Nonlocal Harnack inequalities. J Funct Anal. 2014;267:1807–1836.
   Web of Science ®Google Scholar
• Iannizzotto A, Mosconi S, Squassina M. Hs versus C0-weighted minimizers. Nonlinear Differ Equ Appl. 2014;22:477–497.
   Web of Science ®Google Scholar
• Kuusi T, Mingione G, Sire Y. Nonlocal equations with measure data. Commun Math Phys. 2015;337:1317–1368.
   Web of Science ®Google Scholar
• Lindgren E. Hölder estimates for viscosity solutions of equations of fractional p-Laplace type. NoDEA Nonlinear Differ Equ Appl. 2016;23:Art. 55, 18 pp.
   Web of Science ®Google Scholar
• Iannizzotto A, Liu S, Perera K, et al. Existence results for fractional p-Laplacian problems via Morse theory. Adv Calc Var. 2014;9:101–125.
   Web of Science ®Google Scholar
• Perera K, Squassina M, Yang Y. Bifurcation and multiplicity results for critical fractional p-Laplacian problems. Math Nachr. 2016;289:332–342.
   Web of Science ®Google Scholar
• Xiang MQ, Zhang BL, Radulescu V. Existence of solutions for perturbed fractional p-Laplacian equations. J Differ Equ. 2016;260:1392–1413.
   Web of Science ®Google Scholar
• Alama S, Tarantello G. On semilinear elliptic equations with indefinite nonlinearities. Calc Var Partial Differ Equ. 1993;1):439–475.
   Web of Science ®Google Scholar
• Berestycki H, Capuzzo-Dolcetta I, Niremberg L. Variational methods for indefinite superlinear homogeneous elliptic problems. NoDEA. 1995;2):553–572.
   Google Scholar
• Birindelli I, Demengel F. On some partial differential equation for non-coercive functional and critical Sobolev exponent. Differ Integral Equ. 2002;15:823–837.
   Google Scholar
• Ouyang T. On the positive solutions of semilinear equations Δu+λu−hup=0 on the compact manifolds. Trans Am Math Soc. 1992;331:503–527.
   Web of Science ®Google Scholar
• Birindelli I, Demengel F. Existence of solutions for semilinear equations involving the p-Laplacian: the non-coercive case. Calc Var Partial Differ Equ. 2004;20:343–366.
   Web of Science ®Google Scholar
• de Paiva F, Quoirin H. A superlinear type problem for a p-Laplacian perturbation. Mat Contemp. 2011;40:131–148.
   Google Scholar
• Il'yasov Y. On positive solutions of indefinite elliptic equations. C R Acad Sci Paris Sr I Math. 2001;333:533–538.
   Google Scholar
• Ramos Quoirin H. Lack of coercivity in a concave–convex type equation. Calc Var Partial Differ Equ. 2010;37:523–546.
   Web of Science ®Google Scholar
• Drabek P, Huang YX. Multiple positive solutions of quasilinear elliptic equations in RN. Nonlinear Anal. 1999;37:457–466.
   Web of Science ®Google Scholar
• Chabrowski J, Marcos do Ó J. On some fourth-order semilinear elliptic problems in RN. Nonlinear Anal. 2002;49:861–884.
   Web of Science ®Google Scholar
• Goyal S, Sreenadh K. Existence of multiple solutions of p-fractional Laplace operator with sign-changing weight function. Adv Nonlinear Anal. 2015;4:37–58.
   Web of Science ®Google Scholar
• Fu Y, Li B. On fractional Laplacian problems with indefinite nonlinearity. Appl Anal. 2016;16:2852–2858.
   Google Scholar
• Di Nezza E, Palatucci G, Valdinoci E. Hitchhiker's guide to the fractional Sobolev spaces. Bull Sci Math. 2012;136:521–573.
   Web of Science ®Google Scholar
• Del Pezzo LM, Quaas A. A Hopf's lemma and a strong minimum principle for the fractional p-Laplacian. J Differ Equ. 2017;263:765–778.
   Web of Science ®Google Scholar
• Struve M. Variational methods, applications to nonlinear PDE and Hamiltonian systems. Berlin: Springer-Verlag; 1996.
   Google Scholar
• de Figueiredo DG, Gossez J-P, Ubilla P. Local ‘superlinearity’ and ‘sublinearity’ for the p-Laplacian. J Funct Anal. 2009;257:721–752.
   Web of Science ®Google Scholar
• Wei Y, Su X. Multiplicity of solutions for non-local elliptic equations driven by the fractional Laplacian. Berlin: Springer-Verlag; 2014.
   Google Scholar
• Brasco L, Franzina G. Convexity properties of Dirichlet integrals and picone-type inequalities. Kodai Math J. 2014;37:769–799.
   Web of Science ®Google Scholar