Positive solutions to classes of infinite semipositone (p,q)-Laplace problems with nonlinear boundary conditions

Sim, Inbo; Son, Byungjae

doi:10.1016/j.jmaa.2020.124577

Cited by 6 publications

(2 citation statements)

References 14 publications

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“…Das et al in [14] proved the existence of a positive solution for such a problem in an arbitrary domain when the reaction term is nonsingular. In [40], authors study an infinite semipositone problem for (p, q) Laplacian in an interval using a fixed point theorem. Hai and co-authors in [29] have recently studied a similar equation in a ball by assuming the radial nature of the solution and converting it to an ODE.…”

Section: Introductionmentioning

confidence: 99%

On a class of infinite semipositone problems for (p,q) Laplace operator

Dhanya¹,

Harish²,

Pramanik³

2023

Preprint

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We analyze a non-linear elliptic boundary value problem, that involves (p, q) Laplace operator, for the existence of its positive solution in an arbitrary smooth bounded domain. The non-linearity here is driven by a continuous function in (0, ∞) which is singular, monotonically increasing and eventually positive. We prove the existence of a positive solution of this problem using a fixed point theorem due to Amann[3]. In addition, for a specific nonlinearity we derive that the obtained solution is maximal in nature. The main results obtained here are first of its kind for a (p, q) Laplace operator in an arbitrary bounded domain.

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Section: Introductionmentioning

confidence: 99%

On a class of infinite semipositone problems for (p,q) Laplace operator

Dhanya¹,

Harish²,

Pramanik³

2023

Preprint

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“…Turning to the equations involving the nonhomogeneous operators and singular nonlinearities, in particular, the operator L p,q have been recently investigated in [20,31] and [38,40].…”

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confidence: 99%

Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities

Arora¹

2021

Preprint

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This paper is concerned with the study of multiple positive solutions to the following elliptic problem involving a nonhomogeneous operator with nonstandard growth of p-q type and singular nonlinearitieswhere Ω is a bounded domain inLp,qu := div(|∇u| p−2 ∇u + |∇u| q−2 ∇u), 1 < p < q < ∞, γ ∈ (0, 1), and f is a continuous nondecreasing map satisfying suitable conditions. By constructing two distinctive pairs of strict sub and super solution, and using fixed point theorems by Amann [1], we prove existence of three positive solutions in the positive cone of C δ (Ω) and in a certain range of λ.

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On a class of singular double phase problems with nonnegative weights whose sum can be zero

Sim,

Son

2023

Nonlinear Analysis

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Positive solutions to classes of infinite semipositone (p,q)-Laplace problems with nonlinear boundary conditions

Cited by 6 publications

References 14 publications

On a class of infinite semipositone problems for (p,q) Laplace operator

On a class of infinite semipositone problems for (p,q) Laplace operator

Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities

On a class of singular double phase problems with nonnegative weights whose sum can be zero

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