Existence and multiplicity analysis of a system of nonlinear elliptic equations: Theoretical results and applications

References

[1] G. Bonanno, P. Candito and G. D’Aguì, Variational methods on finite dimensional Banach spaces and discrete problems, Adv. Nonlinear Stud. 14 (2014), no. 4, 915–939. 10.1515/ans-2014-0406Search in Google Scholar

[2] G. Bonanno and S. A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal. 89 (2010), no. 1, 1–10. 10.1080/00036810903397438Search in Google Scholar

[3] Y. Chen, S. Levine and M. Rao, Variable exponent, linear growth functionals in image restoration, SIAM J. Appl. Math. 66 (2006), no. 4, 1383–1406. 10.1137/050624522Search in Google Scholar

[4] E. B. Davies and A. M. Hinz, Explicit constants for Rellich inequalities in L p ⁢ ( Ω ) , Math. Z. 227 (1998), no. 3, 511–523. 10.1007/PL00004389Search in Google Scholar

[5] X.-L. Fan and Q.-H. Zhang, Existence of solutions for p ⁢ ( x ) -Laplacian Dirichlet problem, Nonlinear Anal. 52 (2003), no. 8, 1843–1852. 10.1016/S0362-546X(02)00150-5Search in Google Scholar

[6] X.-L. Fan and D. Zhao, On the generalized Orlicz–Sobolev space W k , p ⁢ ( x ) ⁢ ( Ω ) , J. Gansu Educ. College 12 (1998), 1–6. Search in Google Scholar

[7] A. Hadjian and S. Shakeri, Multiple solutions for a class of Dirichlet double eigenvalue quasilinear elliptic systems involving the ( p 1 , p 2 , … , p n ) -laplacian operator, Sci. World J. 2013 (2013), Article ID 767989. 10.1155/2013/767989Search in Google Scholar PubMed PubMed Central

[8] Y. Karagiorgos and N. Yannakakis, A Neumann problem involving the p ⁢ ( x ) -Laplacian with p = ∞ in a subdomain, Adv. Calc. Var. 9 (2016), no. 1, 65–76. 10.1515/acv-2014-0003Search in Google Scholar

[9] W. Liu and P. Zhao, Existence of positive solutions for p ⁢ ( x ) -Laplacian equations in unbounded domains, Nonlinear Anal. 69 (2008), no. 10, 3358–3371. 10.1016/j.na.2007.09.027Search in Google Scholar

[10] M. Růžička, Electrorheological Fluids: Modeling and Mathematical Theory, Lecture Notes in Math. 1748, Springer, Berlin, 2000. 10.1007/BFb0104029Search in Google Scholar

[11] J. Simon, Régularité de la solution d’une équation non linéaire dans 𝐑 N , Journées d’Analyse Non Linéaire (Besançon 1977), Lecture Notes in Math. 665, Springer, Berlin (1978), 205–227. 10.1007/BFb0061807Search in Google Scholar

[12] Z. Yuan, Y. Wang and S. Liu, Multiplicity of solutions for a class of ( p 1 , p 2 , … , p n ) -Laplacian elliptic systems with a nonsmooth potential, Bound. Value Probl. 2019 (2019), Paper No. 50. 10.1186/s13661-019-1164-6Search in Google Scholar