Abstract
We prove some existence and nonexistence results for a class of critical (p, q)-Laplacian problems in a bounded domain. Our results extend and complement those in the literature for model cases.
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References
Gongbao, L., Zhang, G.: Multiple solutions for the \(p\) & \(q\)-Laplacian problem with critical exponent. Acta Math. Sci. Ser. B (Engl. Ed.) 29(4), 903–918 (2009)
Yin, H., Yang, Z.: Multiplicity of positive solutions to a \(p-q\)-Laplacian equation involving critical nonlinearity. Nonlinear Anal. 75(6), 3021–3035 (2012)
Candito, P., Marano, S.A., Perera, K.: On a class of critical \((p, q)\)-Laplacian problems. NoDEA Nonlinear Diff. Equ. Appl. 22(6), 1959–1972 (2015)
Ho, K., Inbo, S.: An existence result for \((p, q)\)-Laplace equations involving sandwich-type and critical growth. Appl. Math. Lett. 111, 106646 (2021)
Marano, S.A., Mosconi, S.: Some recent results on the Dirichlet problem for \((p, q)\)-Laplace equations. Discrete Contin. Dyn. Syst. Ser. S 11(2), 279–291 (2018)
Guedda, M., Véron, L.: Quasilinear elliptic equations involving critical Sobolev exponents. Nonlinear Anal. 13(8), 879–902 (1989)
Gazzola, F., Ruf, B.: Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations. Adv. Diff. Equ. 2(4), 555–572 (1997)
Arioli, G., Gazzola, F.: Some results on \(p\)-Laplace equations with a critical growth term. Diff. Integral Equ. 11(2), 311–326 (1998)
Drabek, P., Huang, Y.X.: Multiplicity of positive solutions for some quasilinear elliptic equation in \({ R}^N\) with critical Sobolev exponent. J. Diff. Equ. 140(1), 106–132 (1997)
Vázquez, J.L.: A strong maximum principle for some quasilinear elliptic equations. Appl. Math. Optim. 12(3), 191–202 (1984)
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The third author was supported by the 2022-0461 Research Fund of the University of Ulsan.
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Ho, K., Perera, K. & Sim, I. On the Brezis–Nirenberg problem for the (p, q)-Laplacian. Annali di Matematica 202, 1991–2005 (2023). https://doi.org/10.1007/s10231-023-01309-y
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DOI: https://doi.org/10.1007/s10231-023-01309-y