The paper focuses on a parametric quasilinear Dirichlet system exhibiting intertwined exponential nonlinearities. Through the sub-supersolution method, a region of admissible parameters for which there exist bounded positive solutions is identified. As an application, the asymptotic behavior of the solutions is studied when the parameters approach zero.
AlvesC. O.ShenL. (2024). On existence of solutions for some classes of elliptic problems with supercritical exponential growth. Mathematische Zeitschrift, 306(2), 21. Paper No. 29. https://doi.org/10.1007/s00209-023-03420-5
CarlS.LeV. K.MotreanuD. (2007). Nonsmooth variational problems and their inequalities: Comparison principles and applications. Springer.
4.
CarlS.MotreanuD. (2017). Extremal solutions for nonvariational quasilinear elliptic systems via expanding trapping regions. Monatshefte fur Mathematik, 182, 801–821. https://doi.org/10.10.1007/s00605-015-0874-9
5.
De AraujoA. L. A.FariaL. F. O.MedeirosA. H. S.MotreanuD. Positive solutions of nonlinear elliptic equations involving unbounded variable exponents and exponential growth. Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications, 17(2025), 279–295. https://doi.org/10.56082/annalsarscimath.2025.1.279
6.
De AraujoA. L. A.FariaL. F. O.Melo GurjaoJ. L. F. (2020). Positive solutions of nonlinear elliptic equations involving supercrititcal Sobolev exponents without Ambrosetti and Rabinowitz condition. Calculus of Variations and Partial Differential Equations, 59, 18. Paper No. 147.https://doi.org/10.1007/s00526-020-01800-x
7.
De AraujoA. L. A.FariaL. F. O.MotreanuD. (2024a). Positive solutions of nonlinear elliptic equations involving unbounded variable exponents and convection term. Partial Differential Equations and Applications, 5(5), 27. https://doi.org/10.1007/s42985-024-00298-8
8.
De AraujoA. L. A.FariaL. F. O.MotreanuD. (2024b). Quasilinear systems with unbounded variable exponents and convection terms. Bulletin of the Brazilian Mathematical Society, New Series, 55(2), 22. Paper No. 17. https://doi.org/10.1007/s00574-024-00391-x
9.
De AraujoA. L. A.MontenegroM. (2023). Existence of solution for a nonlinear equation with supercritical exponential growth. Journal of Fixed Point Theory and Applications, 25(1), 18. Paper No. 26. https://doi.org/10.1007/s11784-022-01002-2
10.
Do OJ. M.RufB.UbillaP. (2014). On supercritical Sobolev type inequalities and related elliptic equations. Calculus of Variations and Partial Differential Equations, 55, 18. Article No. 83. https://doi.org/10.1007/s00526-016-1015-6
11.
FariaL. F. O.MontenegroM. (2022). Existence of solution for elliptic equations with supercritical Trudinger–Moser growth. Proceedings of the Royal Society of Edinburgh Section A, 152(2), 291–310. https://doi.org/10.1017/prm.2021.4
12.
FariaL. F. O.MontenegroM. (2023). Existence of solution for a supercritical nonlinear Schrodinger equation. Complex Variables and Elliptic Equations, 68, 1–28. https://doi.org/10.1080/17476933.2021.1968383
13.
GiacomoniJ.HernandezJ.SauvyP. (2013). Quasilinear and singular elliptic systems. Advances in Nonlinear Analysis, 2(1), 1C41. https://doi.org/10.1515/anona-2012-0019
14.
LiebermanG. M. (1988). Boundary regularity for solutions of degenerate elliptic equations.. Nonlinear Analysis: Theory Methods & Applications, 12, 1203–1219. https://doi.org/10.1016/0362-546X(88)90053-3
15.
LiuC. L.ZhangX. Y. (2023). Existence and multiplicity of solutions for a quasilinear system with locally superlinear condition. Advances in Nonlinear Analysis, 12(1), 31. Paper No. 20220289.https://doi.org/10.1515/anona-2022-0289
16.
MotreanuD.MotreanuV. V.PapageorgiouN. S. (2011). Multiple constant sign and nodal solutions for nonlinear Neumann eigenvalue problems. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 10(5), 729–755. https://doi.org/10.2422/2036-2145.2011.3.09
SimonJ. (1978). Regularité de la solution d’une équation non linéaire dans . In Journées d’Analyse non linéaire (Proceedings of the Conference, Besancon 1977), Lecture Notes in Mathematics (Vol. 665, pp. 205–227). Springer.