Perturbed eigenvalue problems: an overview
DOI:
https://doi.org/10.24193/subbmath.2021.1.05Keywords:
Eigenvalue problem, p-Laplace operator, nonlocal (s; p)-Laplace oper- ator, Sobolev space, variational methods.Abstract
The study of perturbed eigenvalue problems has been a very active field of investigation throughout the years. In this survey we collect several results in the field.
Mathematics Subject Classiffication (2010): 35D30, 35D40, 46E30, 49J40, 35A15.
References
Abreu, J., Madeira, G.F., Generalized eigenvalues of the (p; 2)-Laplacian under a parametric boundary condition, Proc. Edinb. Math. Soc., 63(2020), 287-303.
Barbu, L., Morosanu, G., Eigenvalues of the negative (p; q)-Laplacian under a Steklov-like boundary condition, Complex Var. Elliptic Equ., 64(2019), 685-700.
Bhattacharya, T., Emamizadeh, B., Farjudian, A., Existence of continuous eigenvalues for a class of parametric problems involving the (p; 2)-Laplacian operator, Acta Appl. Math., 165(2020), 65-79.
Bocea, M., Mihailescu, M., Eigenvalue problems in Orlicz-Sobolev spaces for rapidly growing operators in divergence form, J. Differential Eqnuations, 256(2014), 640-657.
Bocea, M., Mihailescu, M., Existence of nonnegative viscosity solutions for a class of problems involving the 1-Laplacian, Nonlinear Differential Equations and Applications (NoDEA), 23(2016), Art. 11.
Chhetri, M., Drabek, P., Principal eigenvalue of p-Laplacian operator in exterior domain, Results Math., 66(2014), 461-468.
Costea, N., Morosanu, G., Steklov-type eigenvalues of Δp+Δq, Pure Appl. Funct. Anal., 3(2018), 75-89.
Farcaseanu, M., An eigenvalue problem involving an anisotropic differential operator, Complex Variables and Elliptic Equations, 62(2017), 297-306.
Farcaseanu, M., Mihailescu, M., Stancu-Dumitru, D., On the set of eigenvalues of some PDEs with homogeneous Neumann boundary condition, Nonlinear Analysis, 116(2015), 19-25.
Farcaseanu, M., Mihailescu, M., Stancu-Dumitru, D., Perturbed fractional eigenvalue problems, Discrete and Continuous Dynamical Systems - Series A, 37(2017), 6243-6255.
Fukagai, N., Ito, M., Narukawa, K., Limit as p → ∞ of p-Laplace eigenvalue problems and L1-inequality of Poincare type, Differential Integral Equations, 12(1999), 183-206.
Grecu, A., Fractional eigenvalue problems on RN, Electronic Journal of Qualitative Theory of Differential Equations, 26(2020), 1-17.
Grecu, A., A perturbed eigenvalue problem in exterior domain, submitted.
Gyulov, T., Morosanu, G., Eigenvalues of -(Δp + Δq) under a Robin-like boundary condition, Ann. Acad. Rom. Sci. Ser. Math. Appl., 8(2016), 114-132.
Juutinen, P., Lindqvist, P., Manfredi, J.J., The 1-eigenvalue problem, Arch. Rational Mech. Anal., 148(1999), 89-105.
Le, A., Eigenvalue problems for the p-Laplacian, Nonlinear Analysis, 64(2006), 1057-1099.
Lindgren, E., Lindqvist, P., Fractional eigenvalues, Calc. Var., 49(2014), 795-826.
Lindqvist, P., A nonlinear eigenvalue problem, In: Ciatti, Paolo (ed.) et al., "Topics in Mathematical Analysis", 175-203, Hackensack, NJ: World Scientific (ISBN 978-981-281-105-9/hbk). Series on Analysis Applications and Computation 3, 2008.
Mihailescu, M., An eigenvalue problem possessing a continuous family of eigenvalues plus an isolated eigenvalue, Communications on Pure and Applied Analysis, 10(2011), 701-708.
Mihailescu, M., The Spectrum of the Mean Curvature Operator, accepted for publication in: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. (DOI:10.1017/prm.2020.25).
Mihailescu, M., Morosanu, G., Eigenvalues of -Δp - Δq under Neumann boundary condition, Canadian Mathematical Bulletin, 59(2016), 606-616.
Mihailescu, M., Stancu-Dumitru, D., A perturbed eigenvalue problem on general domains, Annals of Functional Analysis, 7(2016), 529-542.
Tanaka, M., Generalized eigenvalue problems for (p; q)-Laplacian with indefinite weight, J. Math. Anal. Appl., 419(2014), 1181-1192.
Szulkin, A., Minimax principles for lower semicontinuous functions and applications to nonlinear boundary value problems, Ann. Inst. H. Poincare Anal. Non Lineaire, 3(1986), 77-109.
Szulkin, A., Willem, M., Eigenvalue problems with indefinite weights, Studia Mathematica, 135(1999), 191-201.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Studia Universitatis Babeș-Bolyai Mathematica
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
