Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
In this paper, we investigate some classes of Neumann fractional p-Laplacian problems. We prove the existence and multiplicity of nontrivial solutions for several different nonlinearities, by using variational methods and critical point theory based on cohomological linking.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
623--645
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
- Southwest University, School of Mathematics and Statistics, Chongqing 400715, P.R. China
autor
- Tuscia University, Department of Ecology and Biology (DEB), Largo dell’Universita, 01100 Viterbo, Italy
autor
- Southwest University, School of Mathematics and Statistics, Chongqing 400715, P.R. China
Bibliografia
- [1] B. Abdellaoui, A. Attar, R. Bentifour, On fractional p-Laplacian parabolic problem with general data, Ann. Mat. Pura Appl. (4) 197 (2018), 329–356.
- [2] A. Audrito, J.-C. Felipe-Navarro, X. Ros-Oton, The Neumann problem for the fractional Laplacian: regularity up to the boundary, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 24 (2023), 1155–1222.
- [3] B. Barrios, E. Colorado, A. De Pablo, U. Sánchez, On some critical problems for the fractional Laplacian operator, J. Differential Equations 252 (2012), 6133–6162.
- [4] B. Barrios, L. Montoro, I. Peral, F. Soria, Neumann conditions for the higher order s-fractional Laplacian (−Δ)su with s > 1, Nonlinear Anal. 193 (2020), 111368.
- [5] P. Bartolo, V. Benci, D. Fortunato, Abstract critical point theorems and applications to some nonlinear problems with strong resonance at infinity, Nonlinear Anal. 7 (1983), 981–1012.
- [6] Z. Binlin, G. Molica Bisci, R. Servadei, Superlinear nonlocal fractional problems with infinitely many solutions, Nonlinearity 28 (2015), 2247–2264.
- [7] T. Chen, W. Liu, Solvability of fractional boundary value problem with p-Laplacian via critical point theory, Bound. Value Probl. 75 (2016), 1–12.
- [8] E. Cinti, F. Colasuonno, Existence and non-existence results for a semilinear fractional Neumann problem, NoDEA Nonlinear Differential Equations Appl. 30 (2023), 79.
- [9] M. Degiovanni, S. Lancellotti, Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity, Ann. Inst. Henri Poincare, Anal. Non Lineaire 24 (2007), 907–919.
- [10] L.M. Del Pezzo, J.D. Rossi, A.M. Salort, Fractional eigenvalue problems that approximate Steklov eigenvalue problems, Proc. R. Soc. Edinb., Sect. A 148 (2018), 499–516.
- [11] E. Di Nezza, G. Palatucci, E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces, Bull. Sci. Math. 136 (2012), 521–573.
- [12] S. Dipierro, X. Ros-Oton, E. Valdinoci, Nonlocal problems with Neumann boundary conditions, Rev. Mat. Iberoam. 33 (2017), 377–416.
- [13] D.E. Edmunds, W.D. Evans, Fractional Sobolev Spaces and Inequalities, Cambridge University Press, 2022.
- [14] E.R. Fadell, P.H. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math. 45 (1978), 139–174.
- [15] M. Frigon, On a new notion of linking and application to elliptic problems at resonance, J. Differ. Equ. 153 (1999), 96–120.
- [16] A. Iannizzotto, S. Liu, K. Perera, M. Squassina, Existence results for fractional p-Laplacian problems via Morse theory, Adv. Calc. Var. 9 (2014), 101–125.
- [17] A. Iannizzotto, M. Squassina, Weyl-type laws for fractional p-eigenvalue problems, Asymptot. Anal. 88 (2014), 233–245.
- [18] J.M. Mazon, J.D. Rossi, J. Toledo, Fractional p-Laplacian evolution equations, J. Math. Pures Appl. 105 (2016), 810–844.
- [19] D. Motreanu, V.V. Motreanu, N. Papageorgiou, Topological and variational methods with applications to nonlinear boundary value problems, Springer, New York, 2014.
- [20] D. Mugnai, Addendum to: Multiplicity of critical points in presence of a linking: application to a superlinear boundary value problem, NoDEA. Nonlinear Differential Equations Appl. 11 (2004), 379–391, and a comment on the generalized Ambrosetti–Rabinowitz condition, NoDEA. Nonlinear Differential Equations Appl. 19 (2012), 299–301.
- [21] D. Mugnai, N.S. Papageorgiou, Wang’s multiplicity result for superlinear (p, q)-equations without the Ambrosetti–Rabinowitz condition, Trans. Amer. Math. Soc. 366 (2014), 4919–4937.
- [22] D. Mugnai, K. Perera, E. Proietti Lippi, A priori estimates for the fractional p-Laplacian with nonlocal Neumann boundary conditions and applications, Comm. Pure Appl. Anal. 21 (2022), 275–292.
- [23] D. Mugnai, A. Pinamonti, E. Vecchi, Towards a Brezis-Oswald-type result for fractional problems with Robin boundary conditions, Calc. Var. Partial Differ. Equ. 59 (2020), 43.
- [24] D. Mugnai, E. Proietti Lippi, Linking over cones for the Neumann fractional p-Laplacian, J. Differential Equations 271 (2021), 797–820.
- [25] D. Mugnai, E. Proietti Lippi, Neumann fractional p-Laplacian: eigenvalues and existence results, Nonlinear Anal. 188 (2019), 455–474.
- [26] D. Mugnai, E. Proietti Lippi, Quasilinear fractional Neumann problems, Mathematics 13 (2025), 85.
- [27] R. Musina, A.I. Nazarov, Strong maximum principles for fractional Laplacians, Proc. Roy. Soc. Edinburgh Sect. A 149 (2019), 1223–1240.
- [28] G. Palatucci, The Dirichlet problem for the p-fractional Laplace equation, Nonlinear Anal. 177 (2018), 699–732.
- [29] P. Piersanti, P. Pucci, Existence theorems for fractional p-Laplacian problems, Anal. Appl. (Singap.) 15 (2017), 607–640.
- [30] P. Stinga, B. Volzone, Fractional semilinear Neumann problems arising from a fractional Keller-Segel model, Calc. Var. Partial Differential Equations 54 (2015), 1009–1042.
- [31] M. Warma, The fractional Neumann and Robin type boundary conditions for the regional fractional p-Laplacian, NoDEA Nonlinear Differ. Equ. Appl. 23 (2016), 1–46.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-bca5c88a-f6b4-424c-ae66-3c2952881eb3
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