Constant sign and nodal solutions for parametric anisotropic (p, 2) -equations

References

• Bahrouni A, Rădulescu VD, Repovš DD. Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves. Nonlinearity. 2019;32:2481–2495.
   Web of Science ®Google Scholar
• Ržička M. Electrorheological fluids: modeling and mathematical theory. Berlin: Springer-Verlag; 2000. (Lecture Notes in Mathematics; 1748).
   Google Scholar
• Zhikov VV. On variational problems and nonlinear elliptic equations with nonstandard growth conditions. J Math Sci. 2011;173:463–570.
   Google Scholar
• Agarwal RP, Alghamdi AM, Gala S, et al. On the continuation principle of local smooth solution for the Hall-MHD equations. Appl Anal. 2020. 9 pp. https://doi.org/10.1080/00036811.2020.1753711.
   Web of Science ®Google Scholar
• Ragusa MA, Tachikawa A. Regularity for minimizers for functionals of double phase with variable exponents. Adv Nonlinear Anal. 2020;9:710–728.
   Web of Science ®Google Scholar
• Gasiński L, Papageorgiou NS. Nonlinear analysis. Boca Raton (FL): Chapman and Hall/CRC Press; 2006. (Series Mathematical Analysis and Applications; 9).
   Google Scholar
• Rădulescu VD, Repovš DD. Partial differential equations with variable exponents: variational methods and qualitative analysis. Boca Raton (FL): Chapman and Hall/CRC Press; 2015.
   Google Scholar
• Rădulescu VD, Isotropic and anisotropic double-phase problems: old and new. Opuscula Math. 2019;39:259–279.
   Web of Science ®Google Scholar
• Papageorgiou NS, Rădulescu VD, Repovš DD. Nonlinear analysis – theory and methods. In: Springer Monographs in Mathematics. Springer, Cham; 2019.
   Google Scholar
• Papageorgiou NS, Scapellato A. Positive solutions for singular (p,q)-equations. Z Angew Math Phys. 2020;71:155.
   Web of Science ®Google Scholar
• Papageorgiou NS, Vetro C. Superlinear (p(z),q(z))-equations. Complex Var Elliptic Equ. 2019;64:8–25.
   Web of Science ®Google Scholar
• Zhang Q, Rădulescu VD. Double phase anisotropic variational problems and combined effects of reaction and absorption terms. J Math Pures Appl. 2018;118:159–203.
   Web of Science ®Google Scholar
• Li F, Rong T, Liang Z. Multiple positive solutions for a class of (2,p)-Laplacian equation. J Math Phys. 2018;59:121506.
   Web of Science ®Google Scholar
• Papageorgiou NS, Vetro C, Vetro F. Solutions and positive solutions for superlinear Robin problems. J Math Phys. 2019;60:101506.
   Web of Science ®Google Scholar
• Papageorgiou NS, Scapellato A. Constant sign and nodal solutions for parametric (p,2)-equations. Adv Nonlinear Anal. 2020;9:449–478.
   Web of Science ®Google Scholar
• Diening L, Harjulehto P, Hästö P, et al. Lebesgue and Sobolev spaces with variable exponents. Heidelberg: Springer-Verlag; 2011. (Lecture Notes in Mathematics; 2017).
   Google Scholar
• Hu S, Papageorgiou NS. Handbook of multivalued analysis, Vol I: theory. Dordrecht: Kluwer Academic Publishers; 1997.
   Google Scholar
• Fan X, Deng S-G. Multiplicity of positive solutions for a class of inhomogeneous Neumann problems involving the p(x)-Laplacian. Nonlinear Differ Equ Appl NoDEA. 2009;16:255–271.
   Web of Science ®Google Scholar
• Gasiński L, Papageorgiou NS. Anisotropic nonlinear Neumann problems. Calc Var. 2011;42:323–354.
   Web of Science ®Google Scholar
• Fan X, Zhao D. A class of De Giorgi type and Hölder continuity. Nonlinear Anal. 1999;36:295–318.
   Web of Science ®Google Scholar
• Tan Z, Fang F. Orlicz-Sobolev versus Hölder local minimizer and multiplicity results for quasilinear elliptic equations. J Math Anal Appl. 2013;402:348–370.
   Web of Science ®Google Scholar
• Fukagai N, Narukawa K. On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems. Ann Mat Pura Appl. 2007;186:539–564.
   Web of Science ®Google Scholar
• Zhang Q. A strong maximum principle for differential equations with nonstandard p(x)-growth conditions. J Math Anal Appl. 2005;312:24–32.
   Web of Science ®Google Scholar
• Papageorgiou NS, Rădulescu VD, Repovš DD. Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential. Discrete Contin Dyn Syst. 2017;37:2589–2618.
   Web of Science ®Google Scholar
• Takáč P, Giacomoni J. A p(x)-Laplacian extension of the Díaz-Saa inequality and some applications. Proc R Soc Edinburgh Sec A. 2019;150:205–232.
   Web of Science ®Google Scholar
• Papageorgiou NS, Rădulescu VD, Repovš DD. Anisotropic equations with indefinite potential and competing nonlinearities. Nonlinear Anal. 2020;201:111861.
   Web of Science ®Google Scholar
• Leonardi S, Papageorgiou NS. On a class of critical Robin problems. Forum Math. 2020;32:95–109.
   Web of Science ®Google Scholar