Singular (p,q)-equations with competing perturbations

References

• Ambrosetti A, Brezis H, Cerami G. Combined effects of concave and convex nonlinearities in some elliptic problems. J Funct Anal. 1994;122:519–543.
   Web of Science ®Google Scholar
• Garcia Azorero JP, Manfredi J, Peral Alonso I. Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations. Commun Contemp Math. 2000;2:385–404.
   Web of Science ®Google Scholar
• Guo Z, Zhang Z. W1,p versus C1 local minimizers and multiplicity results for quasilinear elliptic equations. J Math Anal Appl. 2003;286:32–50.
   Web of Science ®Google Scholar
• Leonardi S, Papageorgiou NS. Positive solutions for nonlinear Robin problems with indefinite potential and competing nonlinearities. Positivity. 2019;24:339–367. doi:10.1007/s11117-019-00681-5.
   Web of Science ®Google Scholar
• Papageorgiou NS, Repovs DD, Vetro C. Nonlinear nonhomogeneous Robin problems with almost critical and partially concave reaction. J Geom Anal. 2019;30:1774–1803. doi:10.1007/s12220-019-00278-0.
   Web of Science ®Google Scholar
• Papageorgiou NS, Zhang C. Noncoercive resonant (p,2)-equations with concave terms. Adv Nonlinear Anal. 2020;9:228–249.
   Web of Science ®Google Scholar
• Marano S, Marino G, Papageorgiou NS. On a Dirichlet problem with (p,q)-Laplacian and parametric concave-convex nonlinearity.J Math Anal Appl. 2019;475:1093–1107.
   Web of Science ®Google Scholar
• Papageorgiou NS, Winkert P. Singular p-Laplacian equations with superlinear perturbation. J Differ Equ. 2019;266:1462–1487.
   Web of Science ®Google Scholar
• Papageorgiou NS, Radulescu VD, Repovs DD. Nonlinear nonhomogeneous singular problems. Calc Var Partial Differ Equ. 2020;59(1):9.
   Web of Science ®Google Scholar
• Papageorgiou NS, Vetro C, Vetro F. Positive solutions for singular (p,2)-equations. Z. Angew. Math. Phys. 2019;70(3):72.
   Web of Science ®Google Scholar
• Papageorgiou NS, Scapellato A. Concave-convex problems for the Robin p-Laplacian plus an indefinite potential. Mathematics. 2020;8(3):421.
   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
• Cahn JW, Hilliard JE. Free energy of a nonuniform system. I. Interfacial free energy. J Chem Phys. 1958;28:258–267.
   Web of Science ®Google Scholar
• Bahrouni A, Radulescu VD, Repovs DD. Double phase transonic flow problems with variable growth: nonlinear patterns and stationary waves. Nonlinearity. 2019;32:2481–2495.
   Web of Science ®Google Scholar
• Benci V, D'Avenia P, Fortunato D, et al. Solitons in several space dimensions: Derrick's problem and infinitely many solutions. Arch Ration Mech Anal. 2000;154:297–324.
   Web of Science ®Google Scholar
• Cherfils L, Ilyasov Y. On the stationary solutions of generalized reaction diffusion equations with p&q-Laplacian. Commun Pure Appl Anal. 2005;4:9–22.
   Web of Science ®Google Scholar
• Fife PC. Mathematical aspects of reacting and diffusing systems. Berlin: Springer; 1979. (Lecture Notes in Biomathematics, vol. 28).
   Google Scholar
• Gasinski L, Papageorgiou NS. Exercises in analysis – part 2: nonlinear analysis. Cham: Springer; 2016.
   Google Scholar
• Papageorgiou NS, Radulescu VD, Repovs DD. Nonlinear analysis–theory and methods. Cham: Springer; 2019. (Springer Monographs in Mathematics).
   Google Scholar
• Li G, Yang C. The existence of a nontrivial solution to a nonlinear elliptic boundary problem of p-Laplacian type without the Ambrosetti-Rabinowitz condition. Nonlinear Anal. 2010;72:4602–4613.
   Web of Science ®Google Scholar
• Ladyzhenskaya OA, Uraltseva NN. Linear and quasilinear elliptic equations. New York: Academic Press; 1968.
   Google Scholar
• Lieberman GM. The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva for elliptic equations. Commun Partial Differ Equ. 1991;16:311–361.
   Web of Science ®Google Scholar
• Pucci P, Serrin J. The maximum principle. Basel: Birkhäuser; 2007.
   Google Scholar
• Diaz JI, Saa JE. Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires [Existence and uniqueness of positive solutions of some quasilinear elliptic equations]. C R Acad Sci Paris Ser I Math. 1987;305:521–524. French.
   Google Scholar
• Gilbarg D, Trudinger NS. Elliptic partial differential equations of second order. 2nd ed. Berlin: Springer-Verlag; 1998.
   Google Scholar
• Gasinski L, Papageorgiou NS. Nonlinear analysis. Boca Raton: Chapman & Hall/CRC; 2006.
   Google Scholar
• Lazer AC, McKenna PJ. On a singular nonlinear elliptic boundary-value problem. Proc Amer Math Soc. 1991;111(3):721–730.
   Web of Science ®Google Scholar
• Zhang Q. A strong maximum principle for differential equations with nonstandard p(x)-growth condition. J Math Anal Appl. 2005;312:24–32.
   Web of Science ®Google Scholar
• Papageorgiou NS, Vetro C, Vetro F. Multiple solutions for parametric double phase Dirichlet problems. Commun Contemp Math. 2021;23(4):2050006. doi:10.1142/S0219199720500066.
   Google Scholar
• Papageorgiou NS, Smyrlis G. A birfurcation-type theorem for singular nonoinear elliptic equations. Methods Appl Anal. 2015;22:147–170.
   Google Scholar
• Gasinski L, Papageorgiou NS. Multiple solutions for nonlinear coercive problems with a nonhomogeneous differential operator and a nonsmooth potential. Set-Valued Var Anal. 2012;20:417–443.
   Web of Science ®Google Scholar
• Hu S, Papageorgiou NS. Handbook of multivalued analysis – volume I: theory. Dordrecht: Kluwer Academic Publishers; 1997.
   Google Scholar