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On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters


Affiliations
  • Babol Noshirvani University of Technology, Department of Mathematics, Babol, Iran, Islamic Republic of
     

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We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form {Δu = α1 (f (v)) - 1/un) + β1(h (u) - 1/un),     x € Ω), -Δv = α2 (g (u)) - 1/vθ) + β2(k (v) - 1/uθ),    x € Ω), u = v =0,  x € δΩ), where Ω is a bounded smooth domain of RN, η, θ ε (0, 1), and α1, α2, β1 and β2 are nonnegative parameters. Here f, g, h, k ε C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) > 0. We use the method of sub-super solutions to prove the existence of positive solution for α1 + β1 and α2 + β2 large.


Keywords

Positive Solutions, Infinite Semipositone Systems, Sub-Super Solutions.
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  • Ja ar Ali, R. Shivaji, Multiple positive solutions for a class of p 􀀀 q-Laplacian systems with multiple parameters and combined nonlinear e ects. Di . Int. Eqs. 22 (2009), no. 7-8, 669-678.

  • H. Berestycki, L.A. Ca arrelli and L. Nirenberg, Inequalities for second-order elliptic equation with application to unbounded domain, I, Duke Math. J. 81 (1996) 467-494.

  • S. Cui, Existence and nonexistence of positive solution for singular semilinear elliptic boudary value problems, Nonlinear Anal. (2000) 149-176.

  • D.S. Hall, M.R. Matthews, J.R. Ensher, C. E. Wieman and E.A. Cornell. Dynamics of component separation in a binary mixture of Bose-Einstein condensates. Phys. Rev. Lett. 81 (1998), 1539-1542.

  • E.K. Lee, R. Shivaji, J. Ye, Classes of in nite semipositone systems, Proc. Roy. Soc. Edinb. 139A (2009) 853-865.

  • E.K. Lee, R. Shivaji, Posiotive solutions for in nit semipositone problems with falling zeros, Nonlinear Analysis, 72 (2010) 4475-4479.

  • E.K. Lee, R. Shivaji, J. Ye, Classes of in nite semipositone n n systems, Di . Int. Eqs, 24(3-4) (2011) 361-370.

  • T.C. Lin and J. Wei, Ground state of N coupled nonlinear Schrodinger equations in Rn, n 3. Commun. Math. Phys. 255 (2005), 629-653.

  • P.L. Lions, On the existence of positive solution of semilinear elliptic equation. SIAM. Rev. 24 (1982) 441-467.

  • J.D. Murray, Mathematical biology. I: An introduction , 3rd edn. Interdisciplinary Applied Mathematics, vol. 17 (springer, 2002).

  • J.D. Murray, Mathematical biology. II. Spatial models and biomedical applications, Interdis- ciplinary Applied Mathematics, vol. 18 (springer, 2003).

  • M. Ramaswamy, R. Shivaji, J. Ye, Positive Solutions for a clases of in nite semipositone problems, Di . Int. Eqs, 20 (12) (2007) 1423-1433.


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  • On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters

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Authors

S. H. Rasouli
, Iran, Islamic Republic of

Abstract


We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form {Δu = α1 (f (v)) - 1/un) + β1(h (u) - 1/un),     x € Ω), -Δv = α2 (g (u)) - 1/vθ) + β2(k (v) - 1/uθ),    x € Ω), u = v =0,  x € δΩ), where Ω is a bounded smooth domain of RN, η, θ ε (0, 1), and α1, α2, β1 and β2 are nonnegative parameters. Here f, g, h, k ε C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) > 0. We use the method of sub-super solutions to prove the existence of positive solution for α1 + β1 and α2 + β2 large.


Keywords


Positive Solutions, Infinite Semipositone Systems, Sub-Super Solutions.

References