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2019 | Vol. 39, no. 2 | 159--174
Tytuł artykułu

Nonlinear elliptic equations involving the p-laplacian with mixed Dirichlet-Neumann boundary conditions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
In this paper, a nonlinear differential problem involving the p-Laplacian operator with mixed boundary conditions is investigated. In particular, the existence of three non-zero solutions is established by requiring suitable behavior on the nonlinearity. Concrete examples illustrate the abstract results.
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Rocznik
Strony
159--174
Opis fizyczny
Bibliogr. 15 poz.
Twórcy
  • University of Messina Department of Engineering C. da Di Dio (S. Agata), 98166 Messina, Italy, bonanno@unime.it
  • University of Messina Department of Engineering C. da Di Dio (S. Agata), 98166 Messina, Italy, dagui@unime.it
  • University of Palermo Department of Mathematics and Computer Science Via Archirafi 34, 90123 Palermo, Italy, angela.sciammetta@unipa.it
Bibliografia
  • [1] G. Barletta, R. Livrea, N.S. Papageorgiou, Bifurcation phenomena for the positive solutions on semilinear elliptic problems with mixed boundary conditions, J. Nonlinear Convex Anal. 17 (2016), 1497-1516.
  • [2] G. Bonanno, P. Candito, Three solutions to a Neumann problem for elliptic equations involving the p-Laplacian, Arch. Math. 80 (2003), 424-429.
  • [3] G. Bonanno, P. Candito, Non-differentiate functionals and applications to elliptic problems with discontinuous nonlinearities, J. Differential Equations 244 (2008), 3031-3059.
  • [4] G. Bonanno, G. D'Agui, Mixed elliptic problems involving the p-Laplacian with nonho-mogeneous boundary conditions, Discrete Contin. Dyn. Syst. 37 (2017) 11, 5797-5817.
  • [5] G. Bonanno, G. D'Agui, N.S. Papageorgiou Infinitely many solutions for mixed elliptic problems involving the p-Laplacian, Adv. Nonlinear Stud. 15 (2015), 939-950.
  • [6] G. Bonanno, S.A. Marano, On the structure of the critical set of non-differentiable functions with a weak compactness condition, Appl. Anal. 89 (2010), 1-10.
  • [7] V. Bonfim, A.F. Neves, A one-dimensional heat equation with mixed boundary conditions, J. Differential Equations 139 (1997), 319-338.
  • [8] E. Colorado, I. Peral, Semilinear elliptic problems with mixed Dirichlet-Neumann boundary conditions, J. Funct. Anal. 199 (2003), 468-507.
  • [9] J. Davila, A strong maximum principle for the Laplace equation with mixed boundary condition, J. Funct. Anal. 183 (2001), 231-244.
  • [10] G. D'Agui, S.A. Marano, N.S. Papageorgiou, Multiple solutions to a Robin problem, with indefinite weight and asymmetric reaction, J. Math. Anal. Appl. 433 (2016) 2, 1821-1845.
  • [11] J. Garcia Azorero, A. Malchiodi, L. Montoro, I. Peral, Concentration of solutions for some singularly perturbed mixed problems: Asymptotics of minimal energy solutions, Ann. I. H. Poincare - AN 27 (2010), 37-56.
  • [12] R. Haller-Dintelmann, H.C. Kaiser, J. Rehberg, Elliptic model problems including mixed boundary conditions and material heterogeneities, J. Math. Pures. Appl. 89 (2008), 25-48.
  • [13] I. Mitrea, M. Mitrea, The Poisson problem with mixed boundary conditions in Sobolev and Besov spaces in non-smooth domains, Trans. Amer. Math. Soc. 359 (2007), 4143-4182.
  • [14] N.S. Papageorgiou, V.D. Radulescu, Nonlinear nonhomogeneous Robin problems with superlinear reaction term, Adv. Nonlinear Stud. 16 (2016), 737-764.
  • [15] N.S. Papageorgiou, V.D. Radulescu, Multiplicity of solutions for nonlinear nonhomogeneous Robin problems, Proc. Amer. Math. Soc. 146 (2018), 601-611.
Typ dokumentu
Bibliografia
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