Existence of solutions for a class of kirchhoff-type problem with triple regime logarithmic nonlinearity
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Abstract
In this paper, we use variational methods to study the existence of nontrivial solutions for a class of Kirchhoff-type elliptic problems driven by the p(x)-Laplacian with triple regime and sign-changing nonlinearity.
The main novelty of this paper is our ability to establish an existence result for a class of Kirchhoff-type problems in which the reaction term is sign-changing and exhibits a triple regime (subcritical, critical, and supercritical).
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References
Fan, X.L., Zhang, Q.H, . (2023). Existence of solutions for p(x)-Laplacian Dirichlet problems,. Nonlinear Anal., 52.
Bartsch, T., Liu, Z, . (2004). On a superlinear elliptic p-Laplacian equation, . J. Differential Equations , 189, 149-175.
Diening, L., Hasto, P., Harjulehto. P, Ruzicka, , . (2017). Lebesgue and Sobolev Spaces with Variable Exponents. Springer Lecture Notes.
De Napoli, P., Mariani, M, . (2003). Mountain pass solutions to equations of p-Laplacian type, . Nonlinear Anal, 54.
Gueda, M., Veron, L, . (1989). Quasilinear elliptic equations involving critical Sobolev exponents . Nonlinear Anal., 13.
Ruadulescu, V.D., Repovs, D.D.,, . (2015). Differential Equations with Variable Exponents: : Variational Methods and Qualitative Analysis. CRC Press, Taylor & Francis Group, Boca Raton FL.
Bahri. A, Coron, J.M, . (1988). On a nonlinear elliptic equation involving the critical Sobolev exponent: The effect of the topology of the domain, . Comm. Pure Appl. Math. , 41, 253-294.
Cui, Z., Yang, Z.,, . (2010). A Neumann problem for quasilinear elliptic equations with logarithmic nonlinearity in a ball,. Complex Variables and Elliptic, 55.
Alves, C.O., Radulescu, V, . (2020). The Lane-Emden equation with variable double-phase and multiple regime, . Proc. Amer. Math. Soc., 148, 2937-2952. https://doi.org/.
de Queiroz, O. S, . (2009). A Neumann problem with logarithmic nonlinearity in a ball. Nonlinear Analysis, 70.
Dinca, D., Jebelean, P., Mawhin, J , . (2001). Variational and topological methods for Dirichlet problems with p-Laplacian. Portugal. Math. , 58, 339-378.
Egnell, H, . (1998). Existence and nonexistence results for m-Laplace equations involving critical Sobolev exponents, . Arch. Rational Mech. Anal. , 57-77.
Alves, C.O., Boudjeriou, T.,, . (2021). Existence of solution for a class of heat equation involving the p(x) Laplacian with triple regime . Z. Angew. Math. Phys., 2(72). https://doi.org/.
Kobayashi, J., Otani, M, . (2004). The principle of symmetric criticality for non-differentiable mappings. J. Funct. Anal.
Tian, S, . (2017). Multiple solutions for the semilinear elliptic equations with the sign-changing logarithmic nonlinearity, . J. Math. Anal. Appl. , 454.
Strauss, W.A.,, . (1977). Existence of solitary waves in higher dimensions, . Comm. Math. Phys. .
Huang, Y, . (1994). Existence of positive solutions for a class of the p-Laplace equations. J. Austral. Math. Soc. Sect. , 36.
Liu, H., Liu, Z., Xiao, Q, . (2018). Ground state solution for a fourth-order nonlinear elliptic problem with logarithmic nonlinearity. Appl. Math. Lett. , 79.
Chen, Y.M., Levine, S., Rao, M, . (2006). Variable exponent, linear growth functionals in image restoration, . 66 (2006). SAIM J. Appl. Math, 66.
Alves, C.O., do O, J.M., Miyagaki, O.H , . (2001). On perturbations of a class of periodic m-Laplacian equation with critical growth, . Nonlinear Anal, 45, 849-863. https://doi.org/.
Garcia, J. A., Peral, I.A., . (1987). Existence and non-uniqueness for the p-Laplacian: Nonlinear eigenvalues, . Comm. Partial Differential Equations, 12.
Zhikov, V.V, . (2011). On variational problems and nonlinear elliptic equations with nonstandard growth conditions . J. Math. Sci., 173.