\((p, q)\)-equations with negative concave terms. (English) Zbl 1501.35232
The paper contains results on the existence of multiple solutions with sign information for a nonlinear Dirichlet problem driven by the \((p,q)\)-Laplacian.
Reviewer: Dumitru Motreanu (Perpignan)
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
References:
| [1] | Aizicovici, S.; Papageorgiou, NS; Staicu, V., Degree theory for operators of monotone type and nonlinear elliptic equations with inequality constraints, Mem. Am. Math. Soc., 196, 915, 70 (2008) · Zbl 1165.47041 |
| [2] | Ambrosetti, A.; Brezis, H.; Cerami, G., Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal., 122, 2, 519-543 (1994) · Zbl 0805.35028 · doi:10.1006/jfan.1994.1078 |
| [3] | de Paiva, FO; Massa, E., Multiple solutions for some elliptic equations with a nonlinearity concave at the origin, Nonlinear Anal., 66, 12, 2940-2946 (2007) · Zbl 1114.35061 · doi:10.1016/j.na.2006.04.015 |
| [4] | Díaz, JI; Saá, JE, Existence et unicité de solutions positives pour certaines équations elliptiques quasilinéaires, C. R. Acad. Sci. Paris Sér. I Math., 305, 12, 521-524 (1987) · Zbl 0656.35039 |
| [5] | García Azorero, JP; Peral Alonso, I.; Manfredi, JJ, Sobolev versus Hölder local minimizers and global multiplicity for some quasilinear elliptic equations, Commun. Contemp. Math., 2, 3, 385-404 (2000) · Zbl 0965.35067 · doi:10.1142/S0219199700000190 |
| [6] | Ghoussoub, N., Duality and Perturbation Methods in Critical Point Theory (1993), Cambridge: Cambridge University Press, Cambridge · Zbl 0790.58002 · doi:10.1017/CBO9780511551703 |
| [7] | Ho, K.; Kim, Y-H; Winkert, P.; Zhang, C., The boundedness and Hölder continuity of solutions to elliptic equations involving variable exponents and critical growth, J. Differ. Equ., 313, 503-532 (2022) · Zbl 1483.35054 · doi:10.1016/j.jde.2022.01.004 |
| [8] | Hu, S.; Papageorgiou, NS, Handbook of Multivalued Analysis (1997), Dordrecht: Kluwer Academic Publishers, Dordrecht · Zbl 0887.47001 · doi:10.1007/978-1-4615-6359-4 |
| [9] | Kajikiya, R., A critical point theorem related to the symmetric mountain pass lemma and its applications to elliptic equations, J. Funct. Anal., 225, 2, 352-370 (2005) · Zbl 1081.49002 · doi:10.1016/j.jfa.2005.04.005 |
| [10] | Lê, A., Eigenvalue problems for the \(p\)-Laplacian, Nonlinear Anal., 64, 5, 1057-1099 (2006) · Zbl 1208.35015 · doi:10.1016/j.na.2005.05.056 |
| [11] | Leonardi, S.; Papageorgiou, NS, On a class of critical Robin problems, Forum Math., 32, 1, 95-109 (2020) · Zbl 1437.35217 · doi:10.1515/forum-2019-0160 |
| [12] | Lieberman, GM, The natural generalization of the natural conditions of Ladyzhenskaya and Ural’ tseva for elliptic equations, Commun. Partial Differ. Equ., 16, 2-3, 311-361 (1991) · Zbl 0742.35028 · doi:10.1080/03605309108820761 |
| [13] | Marano, SA; Mosconi, S., Some recent results on the Dirichlet problem for \((p, q)\)-Laplace equations, Discret. Contin. Dyn. Syst. Ser. S, 11, 2, 279-291 (2018) · Zbl 1374.35137 |
| [14] | Motreanu, D.; Motreanu, VV; Papageorgiou, NS, Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems (2014), New York: Springer, New York · Zbl 1292.47001 · doi:10.1007/978-1-4614-9323-5 |
| [15] | Papageorgiou, NS; Winkert, P., Resonant \((p,2)\)-equations with concave terms, Appl. Anal., 94, 2, 342-360 (2015) · Zbl 1308.35075 · doi:10.1080/00036811.2014.895332 |
| [16] | Papageorgiou, NS; Rădulescu, VD, Nonlinear nonhomogeneous Robin problems with superlinear reaction term, Adv. Nonlinear Stud., 16, 4, 737-764 (2016) · Zbl 1352.35021 · doi:10.1515/ans-2016-0023 |
| [17] | Papageorgiou, NS; Winkert, P., Asymmetric \((p,2)\)-equations, superlinear at \(+\infty \), resonant at \(-\infty \), Bull. Sci. Math., 141, 5, 443-488 (2017) · Zbl 1391.35127 · doi:10.1016/j.bulsci.2017.05.003 |
| [18] | Papageorgiou, NS; Winkert, P., Applied Nonlinear Functional Analysis (2018), Berlin: De Gruyter, Berlin · Zbl 1404.46001 · doi:10.1515/9783110532982 |
| [19] | Papageorgiou, NS; Rădulescu, VD; Repovš, DD, Positive solutions for perturbations of the Robin eigenvalue problem plus an indefinite potential, Discret. Contin. Dyn. Syst., 37, 5, 2589-2618 (2017) · Zbl 1365.35017 · doi:10.3934/dcds.2017111 |
| [20] | Papageorgiou, NS; Rădulescu, VD; Repovš, DD, Asymmetric Robin problems with indefinite potential and concave terms, Adv. Nonlinear Stud., 19, 1, 69-87 (2019) · Zbl 1423.35122 · doi:10.1515/ans-2018-2022 |
| [21] | Papageorgiou, NS; Rădulescu, VD; Repovš, DD, Nonlinear Analysis-Theory and Methods (2019), Cham: Springer, Cham · Zbl 1414.46003 · doi:10.1007/978-3-030-03430-6 |
| [22] | Perera, K., Multiplicity results for some elliptic problems with concave nonlinearities, J. Differ. Equ., 140, 1, 133-141 (1997) · Zbl 0889.35036 · doi:10.1006/jdeq.1997.3310 |
| [23] | Pucci, P.; Serrin, J., The Maximum Principle (2007), Basel: Birkhäuser Verlag, Basel · Zbl 1134.35001 · doi:10.1007/978-3-7643-8145-5 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
