On singular quasilinear problems with sign- changing coefficients

Alotaibi, Trad; Hai, D. D.

doi:10.1080/17476933.2019.1622689

Cited by 2 publications

(1 citation statement)

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“…The approach discussed there cannot be extended to an arbitrary bounded open set as the method entirely depends on the symmetry of the domain. Nevertheless, Hai et al, in a series of papers [1], [25], [26], [27] and [28], has considered similar problems for p-Laplace operator in arbitrary bounded open sets in R N . Interested readers may also refer to [2], [4], [13], [24], and [31] for semilinear or quasilinear elliptic problems with indefinite sign non-linearity in bounded domains.…”

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

View full text Add to dashboard Cite

show abstract

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

Dhanya,

Pramanik,

Harish

2024

ASY

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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 singular, monotonically increasing continuous function in ( 0 , ∞ ) which is eventually positive. The novelty in proving the existence of a positive solution lies in the construction of a suitable subsolution. Our contribution marks an advancement in the theory of existence of positive solutions for infinite semipositone problems in arbitrary bounded domains, whereas the prevailing theory is limited to addressing similar problems only in symmetric domains. Additionally, using the ideas pertaining to the construction of subsolution, we establish the exact behavior of the solutions of “q-sublinear” problem involving ( p , q ) Laplace operator when the parameter λ is very large. The parameter estimate that we derive is non-trivial due to the non-homogeneous nature of the operator and is of independent interest.

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On singular quasilinear problems with sign- changing coefficients

Cited by 2 publications

References 11 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

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

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