Existence Results for Classes of Sublinear Semipositone Problems

Castro, Alfonso; Garner, J. B.; Shivaji, R.

doi:10.1007/bf03322297

Cited by 38 publications

(12 citation statements)

References 3 publications

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“…We prove the existence of at least one positive solution under suitable conditions. Our theorem generalizes the nonsingular semipositone results and methods in papers such as [3] and [4]. To obtain a positive subsolution we modify a construction found in [13].…”

Section: Introductionmentioning

confidence: 75%

Existence and multiplicity of positive solutions for classes of singular elliptic PDEs

Chhetri¹,

Robinson²

2009

Journal of Mathematical Analysis and Applications

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We consider the boundary value problemwhere Ω ⊂ R N is a bounded domain, φ is a nonnegative function in L ∞ (Ω) such that φ > 0 on some subset of Ω of positive measure, and g : [0, ∞) → R is continuous. We establish the existence of three positive solutions when g(0) > 0 (positone), the graph of s α+1 g(s) is roughly S-shaped, and α > 0. We also prove that there exists at least one positive solution when g(0) < 0 (semipositone), g(s) is eventually positive for s > 0, and 0 < α < 1.We employ the method of sub-super solutions to prove our results.

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Section: Introductionmentioning

confidence: 75%

Existence and multiplicity of positive solutions for classes of singular elliptic PDEs

Chhetri¹,

Robinson²

2009

Journal of Mathematical Analysis and Applications

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“…x E Q2; ( In fact, the results of [2] and [3] show that for any smooth bounded region the equations (1.6) r Letting F(t) = ji f(s) ds, we see that E(r) = (~'(r))~/2 + F(u(f))) satisfies E'(r) = -f (u'(t))2 I 0.…”

Section: Introductionmentioning

confidence: 99%

Positive solutions for a concave semipositone Dirichlet problem

Castro

Shivaji

1998

Nonlinear Analysis: Theory, Methods & Applications

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“…When Ω is a smooth bounded domain and f : [0, ∞) → R is a C 1 function, the existence and uniqueness of positive solutions of (3) have been studied extensively in the past (see [1][2][3][4][5][6][8][9][10][11]14]). When f satisfies (H 1 ) and (H 2 ), the existence of a positive solution of (3) was established in [14] when the parameter λ is large.…”

Section: Problems Of the Formmentioning

confidence: 99%

Semipositone problems with falling zeros on exterior domains

Sankar

Sasi

Shivaji

2013

Journal of Mathematical Analysis and Applications

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a b s t r a c tWe study boundary value problems of the formwhere λ is a positive parameter, ∆u = div (∇u) is the Laplacian of u, Ω = {x ∈ R n ; n > 2, |x| > r 0 }, K belongs to a class of C 1 functions such that lim r→∞ K (r) = 0, and f belongs to a class of C 1 functions which are negative at the origin and have falling zeros. We discuss the existence and uniqueness of nonnegative radial solutions when λ is large.

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Existence Results for Classes of Sublinear Semipositone Problems

Cited by 38 publications

References 3 publications

Existence and multiplicity of positive solutions for classes of singular elliptic PDEs

Existence and multiplicity of positive solutions for classes of singular elliptic PDEs

Positive solutions for a concave semipositone Dirichlet problem

Semipositone problems with falling zeros on exterior domains

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