Existence of solutions for (p, q)-Laplacian equations with an indefinite potential

References

• Ambrosetti A, Rabinowitz PH. Dual variational methods in critical point theory and applications. J Funct Anal. 1973;14:349–381. doi: 10.1016/0022-1236(73)90051-7
   Google Scholar
• de Figueiredo DG, Gossez JP, Ubilla P. Multiplicity results for a family of semilinear elliptic problems under local superlinearity and sublinearity. J Eur Math Soc. 2006;8:269–288. doi: 10.4171/JEMS/52
   Web of Science ®Google Scholar
• Papageorgiou NS, Andrade Santos AR, Staicu V. Constant sign and nodal solutions for a class of nonlinear Dirichlet problems. J Math Anal Appl. 2015;422:646–666. doi: 10.1016/j.jmaa.2014.08.041
   Web of Science ®Google Scholar
• Alama S, Tarantello G. Elliptic problems with nonlinearities indefinite in sign. J Funct Anal. 1996;141:159–215. doi: 10.1006/jfan.1996.0125
   Web of Science ®Google Scholar
• Ambrosetti A, Garcia Azorero J, Peral I. Multiplicity results for some nonlinear Elliptic equations. J Funct Anal. 1996;137:219–242. doi: 10.1006/jfan.1996.0045
   Web of Science ®Google Scholar
• Drabek P, Pohozaev SI. Positive solutions for the p-Laplacian: application of the fibering method. Proc R Soc Edinb Sec A. 1997;127:703–726. doi: 10.1017/S0308210500023787
   Web of Science ®Google Scholar
• Pohozaev SI. Nonlinear variational problems via the fibering method. In: Chipot M, editor. Handbook of differential equations: stationary partial differential equations, vol. 5. North Holland: Elsevier; 2008. p. 49–209.
   Google Scholar
• Gasiński L, Papageorgiou NS. Dirichlet problems with double resonance and an indefinite potential. Nonlinear Anal. 2012;75(12):4560–4595. doi: 10.1016/j.na.2011.09.014
   Web of Science ®Google Scholar
• Gasiński L, Papageorgiou NS. Dirichlet problems with an indefinite and unbounded potential and concave–convex nonlinearities. Abstr Appl Anal. 2012;2012:36. Art. ID 492025.
   Google Scholar
• Kyritsi STh, Papageorgiou NS. Multiple solutions for superlinear Dirichlet problems with an indefinite potential. Ann Mat. 2013;192:297–315. doi: 10.1007/s10231-011-0224-z
   Google Scholar
• Faria LFO, Miyagaki OH, Tanaka M. Existence of a positive solution for problems with (p,q)-Laplacian and convection term in Rn. Bound Value Probl. 2016;2016(1):158. doi: 10.1186/s13661-016-0665-9
   Google Scholar
• Marano SA, Mosconi SJN. Some recent results on the Dirichlet problem for (p,q)-Laplace equations. Discrete Contin Dyn Syst Ser. 2018;S11(2):279–291. doi: 10.3934/dcdss.2018015
   Google Scholar
• Marano SA, Mosconi SJN, Papageorgiou NS. Multiple solutions to (p,q)-Laplacian problems with resonant concave nonlinearity. Adv Nonlinear Stud. 2016;16:51–65. doi: 10.1515/ans-2015-5011
   Web of Science ®Google Scholar
• Papageorgiou NS, Radulescu VD, Repovs DD. Double-phase problems with reaction of arbitrary growth. Z Angew Math Phys. 2018;69:108. doi: 10.1007/s00033-018-1001-2
   Web of Science ®Google Scholar
• Tanaka M. Generalized eigenvalue problems for (p,q)-Laplacian with indefinite weight. J Math Anal Appl. 2014;419:1181–1192. doi: 10.1016/j.jmaa.2014.05.044
   Google Scholar
• Radulescu VD. Isotropic and anisotropic double-phase problems: old and new. Opuscula Math. 2019;39:259–279. doi: 10.7494/OpMath.2019.39.2.259
   Web of Science ®Google Scholar
• Cencelj M, Radulescu VD, Repovs DD. Double phase problems with variable growth. Nonlinear Anal. 2018;177:270–287. doi: 10.1016/j.na.2018.03.016
   Web of Science ®Google Scholar
• Zhang Q, Radulescu V. Double phase anisotropic variational problems and combined effects of reaction and absorption terms. J Math Pures Appl. 2018;118C:159–203. doi: 10.1016/j.matpur.2018.06.015
   Google Scholar
• Papageorgiou NS, Kyritsi-Yiallourou STh. Handbook of applied analysis. New York (NY): Springer; 2009.
   Google Scholar
• del Pezzo LM, Fernandez Bonder J. An optimization problem for the first eigenvalue of the p-Laplacian plus a potential. Commun Pure Appl Anal. 2006;5(4):675–690. doi: 10.3934/cpaa.2006.5.675
   Web of Science ®Google Scholar
• Mugnai D, Papageorgiou NS. Resonant nonlinear Neumann problems with indefinite weight. Ann Sc Norm Super Pisa Cl Sci (5). 2012;11:729–788.
   Google Scholar
• Drabek P, Hernandez J. Existence and uniqueness of positive solutions for some quasilinear elliptic problems. Nonlinear Anal. 2001;44:189–204. doi: 10.1016/S0362-546X(99)00258-8
   Web of Science ®Google Scholar
• Clark DC. A variant of the Lusternik–Schnirelman theory. Indiana Univ Math J. 1972;22(1):65–74. doi: 10.1512/iumj.1973.22.22008
   Web of Science ®Google Scholar