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Positive solutions for the one-dimensional p-Laplacian with nonlinear boundary conditions

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Języki publikacji
EN
Abstrakty
EN
We prove the existence of positive solutions for the p-Laplacian problem [formula] where [formula] can be nonlinear, i=1,2 , f:(0,∞)→R is p-superlinear or p-sublinear at ∞ and is allowed be singular (±∞) at 0, and λ is a positive parameter.
Rocznik
Strony
675--689
Opis fizyczny
Bibliogr. 19n poz.
Twórcy
autor
  • Mississippi State University Department of Mathematics and Statistics Mississippi State, MS 39762, USA
autor
  • Mississippi State University Department of Mathematics and Statistics Mississippi State, MS 39762, USA
Bibliografia
  • [1] R. Agarwal, D. O'Regan, Semipositone Dirichlet boundary value problems with singular nonlinearities, Houston J. Math. 30 (2004), 297-308.
  • [2] R. Agarwal, D. Cao, H. Lu, Existence and multiplicity of positive solutions for singular semipositone p-Laplacian equations, Can. J. Math. 58 (2006), 449-475.
  • [3] W. Allegretto, P. Nistri, P. Zecca, Positive solutions for elliptic nonpositone problems, Differential Integral Equations 5 (1992), 95-101.
  • [4] H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach Spaces, SIAM Rev. 18 (1976), 620-709.
  • [5] A. Ambrosetti, D. Arcoya, B. Buffoni, Positive solutions for some semipositone problems via bifurcation theory, Differential Integral Equations 7 (1994), 655-663.
  • [6] V. Anurada, D.D. Hai, R. Shivaji, Existence results for superlinear semipositone BVP's, Proc. Amer. Math. Soc. 124 (1996), 757-763.
  • [7] D. Arcoya, A. Zertiti, Existence and nonexistence of radially symmetric nonnegative solutions for a class of semipositone problems in an annulus, Rend. Mat. 14 (1994), 625-646.
  • [8] L. Erbe, H. Wang, On the existence of positive solutions of ordinary differential equations, Proc. Amer. Math. Soc. 120 (1994) 3, 743-748.
  • [9] D.D. Hai, On singular Sturm-Liouville boundary-value problems, Proc. Roy. Soc. Edinburgh Sect. A 140 (2010) 1, 49-63.
  • [10] D.D. Hai, Existence of positive solutions for singular p-Laplacian Sturm-Liouville boundary value problems, Electron. J. Differential Equations (2016), paper no. 260.
  • [11] J. Jacobsen, K. Schmitt, Radial solutions of quasilinear elliptic differential equations, Handbook of Differential Equations, vol. 1, North-Holland, 2004, 359-435.
  • [12] K. Lan, X. Yang, G. Yang, Positive solutions of one-dimensional p-Laplacian equations and applications to population models of one species, Topol. Methods Nonlinear Anal. 46 (2015), 431-445.
  • [13] E. Lee, R. Shivaji, J. Ye, Subsolutions: A journey from positone to infinite semipositone problems, Electron. J. Differ. Equ. Conf. 17 (2009), 123-131.
  • [14] Y. Liu, Twin solutions to singular semipositone problems, J. Math. Anal. Appl. 286 (2003), 248-260.
  • [15] J. Smoller, A. Wasserman, Existence of positive solutions for se.miline.ar elliptic equations in general domains, Arch. Ration. Mech. Anal. 98 (1987), 229-249.
  • [16] J.R.L. Webb, K.Q. Lan, Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary vale problems of local and nonlocal types, Topol. Methods Nonlinear Anal. 27 (2006), 91-116.
  • [17] J. Wang, The existence of positive solutions for the one-dimensional p-Laplacian, Proc. Amer. Math. Soc. 125 (1997), 2275-2283.
  • [18] G.C. Yang, P.F. Zhou, A new existence results of positive solutions for the Sturm-Liouville boundary value problem, Appl. Math. Lett. 23 (2010), 1401-1406.
  • [19] Q. Yao, An existence theorem of a positive solution to a semipositone Sturm-Liouville boundary value problem, Appl. Math. Lett. 23 (2010), 1401-1406.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-06292cc4-ce69-44ff-93f0-e6faead74102
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