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Existence results for Kirchhoff type systems with singular nonlinearity

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using the method of sub-super solutions, we study the existence of positive solutions for a class of singular nonlinear semipositone systems involving nonlocal operator.
Rocznik
Strony
187--199
Opis fizyczny
Bibliogr. 22 poz.
Twórcy
autor
  • Pyame Noor University Faculty of Basic Sciences Department of Mathematics Tehran,Iran
  • Department of Mathematics Faculty of Mathematical Sciences University of Mazandaran Babolsar, Iran
autor
  • Department of Mathematics Faculty of Basic Sciences Pyame Noor Uni
Bibliografia
  • [1] G.A. Afrouzi, N.T. Chung, S. Shakeri, Existence of positive solutions for Kirchhoff type equations, Electron. J. Differential Equations 180 (2013), 1-8.
  • [2] G.A. Afrouzi, N.T. Chung, S. Shakeri, Existence of positive solutions for Kirchhoff type systems with singular weights, submitted.
  • [3] C. Atkinson, K. El Kalli, Some boundary value problems for the Bingham model, J. Non-Newtonian Fluid Mech. 41 (1992), 339-363.
  • [4] L. Caffarelli, R. Kohn, L. Nirenberg, First order interpolation inequalities with weights, Compos. Math. 53 (1984), 259-275.
  • [5] A. Canada, P. Drabek, J.L. Gamez, Existence of positive solutions for some problems with nonlinear diffusion, Trans. Amer. Math. Soc. 349 (1997), 4231-4249.
  • [6] N.T. Chung, An existence result for a class of Kirchhoff type systems via sub and supersolutions method, Appl. Math. Lett. 35 (2014), 95-101.
  • [7] F. Cirstea, D. Motreanu, V. Radulescu, Weak solutions of quasilinear problems with nonlinear boundary condition, Nonlinear Anal. 43 (2001), 623-636.
  • [8] P. Drabek, J. Hernandez, Existence and uniqueness of positive solutions for some quasilinear elliptic problem, Nonlinear Anal. 44 (2001), 189-204.
  • [9] P. Drabek, P. Krejci, P. Takac, Nonlinear Differential Equations, Chapman Hall/CRC Research Notes in Mathematics, vol. 404, Chapman Hall/CRC, Florida, 1999.
  • [10] J. Garcia-Melian, L. Iturriaga, Some counter examples related to the stationary Kirchhoff equations, Proc. Amer. Math. Soc. 144 (2016), 3405-3411.
  • [11] X. Han, G. Dai, On the sub-supersolution method for p(x)-Kirchhoff type equations, Journal ol Inequalities and Applications 2012, (2012):283.
  • [12] G. Kirchhoff, Mechanik, Teubner, Leipzig, Germany, 1883.
  • [13] E.K. Lee, R. Shivaji, J. Ye, Positive solutions for infinite semipositione problems with falling zeros, Nonlinear Anal. 72 (2010), 4475-4479.
  • [14] O.H. Miyagaki, R.S. Rodrigues, On positive solutions for a class of singular quasilinear elliptic systems, J. Math. Anal. Appl. 334 (2007), 818-833.
  • [15] G. Molica Bisci, D. Repovs, Higher nonlocal problems with bounded primitive, J. Math. Anal. Appl. 420 (2014), 167-176.
  • [16] G. Molica Bisci, D. Repovs, Multiple solutions for elliptic equations involving a general operator in divergence form, Ann. Acad. Fenn. Math. 39 (2014), 259-273.
  • [17] G. Molica Bisci, D. Repovs, Existence and localization of solutions for nonlocal fractional equations, Asymptot. Anal. 9 (2014), 367-378.
  • [18] G. Molica Bisci, V. Radulescu, R. Servadei, Variational Methods for Nonlocal Fractional Problems, Encyclopedia ol Mathematics and its Applications, vol. 162, Cambridge University Press, Cambridge, 2016.
  • [19] P. Pucci, B. Zhang, M. Xianq, Existence and multiplicity of entire solutions for fractional p-Kirchhoff equations, Advances in Nonlinear Analysis 5 (2016), 27-55.
  • [20] S.H. Rasouli, A population biological model with a singular nonlinearity, Appl. Math. 59 (2014) 3, 257-264.
  • [21] B. Xuan, The eigenvalue problem for a singular quasilinear elliptic equation, Electron. J. Differential Equations 16 (2004), 1-11.
  • [22] B. Xuan, The solvability of quasilinear Brezis-Nirenberg-type problems with singular-weights, Nonlinear Anal. 62 (2005), 703-725.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-10c3e35b-7a09-46d6-89c8-ffe7793d74a1
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