Multiple solution for a fourth-order nonlinear eigenvalue problem with singular and sublinear potential
DOI:
https://doi.org/10.24193/subbmath.2023.1.10Keywords:
Riemannian manifolds, Schroödinger system, variational arguments, isometries.Abstract
Let (M, g) be a Cartan-Hadamard manifold. For certain positive numbers µ and λ, we establish the multiplicity of solutions.
Mathematics Subject Classification (2010): 54AXX.
Received 04 December 2022; Revised 08 February 2023. Published Online: 2023-03-20. Published Print: 2023-04-30
References
Abdelwaheb, D., Ramzi, A., Existence and multiplicity of solutions for a singular problem involving the p-biharmonic operator in RN , J. Math. Anal. Appl., 499(2021), no. 2, Paper No. 125049, 19 pp.
Bonanno, G., Some remarks on a three critical points theorem, Nonlinear Anal., 54(2003), no. 4, 651–665.
Chaharlang, M., Razani, A., A fourth order singular elliptic problem involving p-biharmonic operator, Taiwanese J. Math., 23(2019), no. 3, 589–599.
d’Avenia, P., Pomponio, A., Schino, J., Radial and non-radial multiple solutions to a general mixed dispersion NLS equation, to appear in Nonlinearity, 2023.
Donatelli, M., Vilasi, L., Existence of multiple solutions for a fourth-order problem with variable exponent, Discrete Contin. Dyn. Syst. Ser. B, 27(2022), no. 5, 2471–2481.
El Khalil, A., Laghzal, M., Morchid, A., Touzani, A., Eigenvalues for a class of singular problems involving p(x)-biharmonic operator and q(x)-Hardy potential, Adv. Nonlinear Anal., 9(2020), no. 1, 1130–1144.
Farkas, C., Kristály, A., Schrödinger-Maxwell systems on non-compact Riemannian manifolds, Nonlinear Anal. Real World Appl., 31(2016), 473–491.
Farkas, C., Kristály, A., Mester, Á., Compact Sobolev embeddings on non-compact manifolds via orbit expansions of isometry groups, Calc. Var. Partial Differential Equations, 60(2021): 128.
Fernández, A.J., Jeanjean, L., Mandel, R., Maris, M., Non-homogeneous Gagliardo-Nirenberg inequalities in RN and application to a biharmonic non-linear Schrödinger equation, J. Differential Equations, 330(2022), 1–65.
Jinguo, Z., Tsing-San, H., Multiplicity results for biharmonic equations involving multiple Rellich-type potentials and critical exponents, Bound. Value Probl., (2019), Paper No. 103, 19 pp.
Kang, D., Liangshun, X., Asymptotic behavior and existence results for the biharmonic problems involving Rellich potentials, J. Math. Anal. Appl., 455(2017), no. 2, 1365-1382.
Kang, D., Xu, L., Biharmonic systems involving multiple Rellich-type potentials and critical Rellich-Sobolev nonlinearities, Commun. Pure Appl. Anal., 17(2018), no. 2, 333- 346.
Karpman, V.I., Shagalov, A.G., Stability of solitons described by nonlinear Schrödinger-type equations with higher-order dispersion, Physica D. Nonlinear Phenomena, 144(2000), no. 1-2, 194–210.
Kristály, A., Rădulescu, V.D., Varga, C.G., Variational Principles in Mathematical Physics, Geometry, and Economics, vol. 136 of Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 2010.
Kristály, A., Repovs, D., Quantitative Rellich inequalities on Finsler-Hadamard manifolds, Commun. Contemp. Math., 18(2016), no. 6, 1650020, 17 pp.
Lin, L., Wen-Wu, P., A note on nonlinear fourth-order elliptic equations on RN , J. Global Optim., 57(2013), no. 4, 1319–1325.
Mousomi, B., Entire solutions for a class of elliptic equations involving p-biharmonic operator and Rellich potentials, J. Math. Anal. Appl., 423(2015), no. 2, 1570–1579.
Mousomi, B., Musina, R., Entire solutions for a class of variational problems involving the biharmonic operator and Rellich potentials, Nonlinear Anal., 75(2012), no. 9, 3836–3848.
Ricceri, B., Existence of three solutions for a class of elliptic eigenvalue problems, Math. Comput. Modelling, 32(11-13)(2000), 1485–1494.
Ricceri, B., On a three critical points theorem, Arch. Math. (Basel), 75(3)(2000), 220–226.
Skrzypczak, L., Tintarev, C., A geometric criterion for compactness of invariant subspaces, Arch. Math. (Basel), 101(3)(2013), 259–268.
Tintarev, C., Concentration Compactness: Functional-Analytic Theory of Concentration Phenomena, De Gruyter, Berlin, Boston, 2020.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2023 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
