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Nontrivial solutions for Neumann fractional p-Laplacian problems

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
623--645
Opis fizyczny
Bibliogr. 31 poz.
Twórcy
autor
  • Southwest University, School of Mathematics and Statistics, Chongqing 400715, P.R. China
  • 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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