ON A CLASS OF SINGULAR P-LAPLACIAN SEMIPOSITONE PROBLEMS WITH SIGN-CHANGING WEIGHT

S. H. Rasouli; Z. Firouzjahi

doi:10.11948/2014021

2014 Volume 4 Issue 4

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S. H. Rasouli, Z. Firouzjahi. ON A CLASS OF SINGULAR P-LAPLACIAN SEMIPOSITONE PROBLEMS WITH SIGN-CHANGING WEIGHT[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 383-388. doi: 10.11948/2014021

Citation:

S. H. Rasouli, Z. Firouzjahi. ON A CLASS OF SINGULAR P-LAPLACIAN SEMIPOSITONE PROBLEMS WITH SIGN-CHANGING WEIGHT[J]. Journal of Applied Analysis & Computation, 2014, 4(4): 383-388. doi: 10.11948/2014021

ON A CLASS OF SINGULAR P-LAPLACIAN SEMIPOSITONE PROBLEMS WITH SIGN-CHANGING WEIGHT

Department of Mathematics, Faculty of Basic Sciences, Babol University of Technology, Babol, Iran

Abstract

Abstract

We study existence of positive weak solution for a class of p-Laplacian problem
{-∆_pu=λg(x)[f(u) -1/u^α], x ∈Ω,
u=0, x ∈ ∂Ω,
where λ is a positive parameter and α ∈ (0, 1); Ω is a bounded domain in R^N for (N>1) with smooth boundary, ∆_pu=div(|∇u|^p-2∇u) is the p-Laplacian operator for (p>2), g(x) is C¹ sign-changing function such that maybe negative near the boundary and be positive in the interior and f is C¹ nondecreasing function lim_s→∞ f(s)/s^p-1=0.We discuss the existence of positive weak solution when f and g satisfy certain additional conditions. We use the method of sub-supersolution to establish our result.
- Positive solution /
- singular problem /
- sub-supersolution
MSC: 35J55;35J65

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References

[1]	J.I. Diaz, Nonlinear Partial Differential Equations And Free Boundaries, Vol. I, vol. 106 of Pitman Research Notes in Mathematics, Pitman, Boston, MA, 1985. Google Scholar
[2]	P. Drabek and J. Hernandez, Existence and uniqueness of positive solutions for some quasilinear elliptic problems, Nonlinear. Analysis, 44(2001), 189-204. Google Scholar
[3]	S. Gui, Existence and nonexistence of positive solution for singular semilinear elliptic boudary value problems, Nonlinear Anal, 2000, 149-176. Google Scholar
[4]	E.K. Lee and R. Shivaji, Positive solutions for infinit semipositone problems with falling zeros, Nonlinear Analysis,72(2010), 4475-4479. Google Scholar
[5]	E.K. Lee, R. Shivaji and J. Ye, Classes of infinite semipositone n×n systems,Diff. Int. Eqs, 24(3-4)(2011), 361-370. Google Scholar
[6]	M. Ramaswamy, R. Shivaji and J. Ye, Positive solution for a class of infinite semipositone problems, Diff. Integ. Eqns, 20(2007), 1423-1433. Google Scholar
[7]	S.H. Rasouli, Z. Halimi and Z. Mashhadban, A remark on the existence of positive weak solution for a class of (p,q)-Laplacian nonlinear system with signchanging weight, Nonl. Anal, 73(2010), 385-389. Google Scholar
[8]	R. Shivaji and J. Ye, Positive solutions for a class of infinite semipositone problems, Differential and Integral Equations, 12(2007), 1423-1433. Google Scholar