Lyapunov-type inequalities for partial differential equations with 𝑝-Laplacian

References

[1] L. Brasco, On principal frequencies and inradius in convex sets, Bruno Pini Mathematical Analysis Seminar 2018, Bruno Pini Math. Anal. Semin. 9, University of Bologna, Bologna (2018), 78–101. 10.1007/s00030-019-0614-2Search in Google Scholar

[2] L. Brasco, On principal frequencies and isoperimetric ratios in convex sets, preprint (2019), http://cvgmt.sns.it/paper/3891/. 10.5802/afst.1653Search in Google Scholar

[3] L. Brasco and G. Franzina, An anisotropic eigenvalue problem of Stekloff type and weighted Wulff inequalities, NoDEA Nonlinear Differential Equations Appl. 20 (2013), no. 6, 1795–1830. 10.1007/s00030-013-0231-4Search in Google Scholar

[4] L. Brasco, C. Nitsch and C. Trombetti, An inequality à la Szegő–Weinberger for the 𝑝-Laplacian on convex sets, Commun. Contemp. Math. 18 (2016), no. 6, Article ID 1550086. 10.1142/S0219199715500868Search in Google Scholar

[5] A. Cañada, J. A. Montero and S. Villegas, Liapunov-type inequalities and Neumann boundary value problems at resonance, Math. Inequal. Appl. 8 (2005), no. 3, 459–475. 10.7153/mia-08-42Search in Google Scholar

[6] A. Cañada, J. A. Montero and S. Villegas, Lyapunov inequalities for partial differential equations, J. Funct. Anal. 237 (2006), no. 1, 176–193. 10.1016/j.jfa.2005.12.011Search in Google Scholar

[7] S. S. Cheng, A discrete analogue of the inequality of Lyapunov, Hokkaido Math. J. 12 (1983), no. 1, 105–112. 10.14492/hokmj/1381757783Search in Google Scholar

[8] P. L. de Nápoli and J. P. Pinasco, Lyapunov-type inequalities for partial differential equations, J. Funct. Anal. 270 (2016), no. 6, 1995–2018. 10.1016/j.jfa.2016.01.006Search in Google Scholar

[9] A. V. Dem’yanov and A. I. Nazarov, On the existence of an extremal function in Sobolev embedding theorems with a limit exponent (in Russian), Algebra i Analiz 17 (2005), no. 5, 105–140; translation in Math. J. 17 (2006), no. 5, 773–796. Search in Google Scholar

[10] J. Edward, S. Hudson and M. Leckband, Existence problems for the 𝑝-Laplacian, Forum Math. 27 (2015), no. 2, 1203–1225. 10.1515/forum-2012-0142Search in Google Scholar

[11] J. Edward, S. Hudson and M. Leckband, Minimal potential results for Schrödinger equations with Neumann boundary conditions, Forum Math. 29 (2017), no. 6, 1337–1348. 10.1515/forum-2015-0082Search in Google Scholar

[12] A. Elbert, A half-linear second order differential equation, Qualitative Theory of Differential Equations, Vol. I, II (Szeged 1979), Colloq. Math. Soc. János Bolyai 30, North-Holland, Amsterdam (1981), 153–180. 10.1007/BF01951012Search in Google Scholar

[13] R. A. C. Ferreira, A Lyapunov-type inequality for a fractional boundary value problem, Fract. Calc. Appl. Anal. 16 (2013), no. 4, 978–984. 10.2478/s13540-013-0060-5Search in Google Scholar

[14] L. Gasiński and N. S. Papageorgiou, Nonlinear Analysis, Ser. Math. Anal. Appl. 9, Chapman & Hall/CRC, Boca Raton, 2006. Search in Google Scholar

[15] E. Giusti, Direct Methods in the Calculus of Variations, World Scientific, River Edge, 2003. 10.1142/5002Search in Google Scholar

[16] M. Hashizume, Minimization problem related to a Lyapunov inequality, J. Math. Anal. Appl. 432 (2015), no. 1, 517–530. 10.1016/j.jmaa.2015.06.031Search in Google Scholar

[17] M. Hashizume and F. Takahashi, Lyapunov inequality for an elliptic problem with the Robin boundary condition, Nonlinear Anal. 129 (2015), 189–197. 10.1016/j.na.2015.08.006Search in Google Scholar

[18] M. Jleli, M. Kirane and B. Samet, Lyapunov-type inequalities for fractional partial differential equations, Appl. Math. Lett. 66 (2017), 30–39. 10.1016/j.aml.2016.10.013Search in Google Scholar

[19] E. H. Lieb and M. Loss, Analysis, 2nd ed., Grad. Stud. Math. 14, American Mathematical Society, Providence, 2001. Search in Google Scholar

[20] S. A. Timoshin, Lyapunov inequality for elliptic equations involving limiting nonlinearities, Proc. Japan Acad. Ser. A Math. Sci. 86 (2010), no. 8, 139–142. 10.3792/pjaa.86.139Search in Google Scholar