Remarks on sublinear elliptic equations

Brezis, Haı̈m; Oswald, Luc

doi:10.1016/0362-546x(86)90011-8

Cited by 433 publications

(386 citation statements)

References 8 publications

Supporting

Mentioning

371

Contrasting

Order By: Relevance

“…The uniqueness follows because the map w → µ(1 − e χv w) is decreasing when µ > 0, see [5]. In the case µ = 0 the equation (48) is linear, and hence it is clear the uniqueness result.…”

Section: Definition 53mentioning

confidence: 89%

On a parabolic–elliptic chemotactic model with coupled boundary conditions

Delgado¹,

Suárez²,

Tello³

2010

Nonlinear Analysis: Real World Applications

View full text Add to dashboard Cite

This paper deals with a nonlinear system of parabolic-elliptic type with a logistic source term and coupled boundary conditions related to pattern formation. We prove the existence of a unique positive global in time classical solution. We analyze also the stationary problem associated. Moreover it is proved, under the assumption of sufficiently strong logistic dumping, that there is only one nonzero homogeneous equilibrium, and all the solutions to the non-stationary tend to this steady-state for large times.

show abstract

Section: Definition 53mentioning

confidence: 89%

On a parabolic–elliptic chemotactic model with coupled boundary conditions

Delgado¹,

Suárez²,

Tello³

2010

Nonlinear Analysis: Real World Applications

View full text Add to dashboard Cite

show abstract

“…In this section we prove the uniqueness of positive solution of (1) under a certain condition on f , extending the result of [2,7,14,16] to the case of quasilinear equations.…”

Section: A Uniqueness Resultsmentioning

confidence: 80%

“…We present here a result of uniqueness of positive solutions for (1) which generalizes a classical one for semilinear equations, see for instance [2,7,14], [16] (Theorems 7.14, 7.15), [24] (page 39) and the references therein. Our proof makes use of the sweeping method of Serrin ([25], page 12), as in [16,24].…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness of positive solution of a logistic equation with nonlinear gradient term

Ruiz

Suárez

2007

Proceedings of the Royal Society of Edinburgh: Section A Mathem

View full text Add to dashboard Cite

show abstract

“…Thanks to the sub and supersolution method, they showed that equation (1.2) has a unique positive classical solution which satisfies homogeneous Dirichlet boundary conditions. Moreover, by applying Karamata regular variation theory, they improved and extended the estimates established in [2,8,14]. On the other hand when α = 0 and the equation (1.2) involves a degenerate operator p-Laplacian, Cavalheiro in [3] proved the existence and uniqueness solution under a suitable condition on the function a.…”

mentioning

confidence: 83%

Positive solutions with specific asymptotic behavior for a polyharmonic problem on Rn

Dhifli¹

2015

OpMath

View full text Add to dashboard Cite

Abstract. This paper is concerned with positive solutions of the semilinear polyharmonic equation (−∆) m u = a(x)u α on R n , where m and n are positive integers with n > 2m, α ∈ (−1, 1). The coefficient a is assumed to satisfyWe prove the existence of a positive solution u such thatwith λ := min(n − 2m, λ−2m 1−α ) and a function L, given explicitly in terms of L and satisfying the same condition at infinity. (Given positive functions f and g on R n , f ≈ g means that c −1 g ≤ f ≤ cg for some constant c > 1.)

show abstract

Remarks on sublinear elliptic equations

Cited by 433 publications

References 8 publications

On a parabolic–elliptic chemotactic model with coupled boundary conditions

On a parabolic–elliptic chemotactic model with coupled boundary conditions

Existence and uniqueness of positive solution of a logistic equation with nonlinear gradient term

Positive solutions with specific asymptotic behavior for a polyharmonic problem on Rn

Contact Info

Product

Resources

About