Existence of two weak solutions for some singular elliptic problems

Khodabakhshi, Mehdi; Aminpour, A. M.; Afrouzi, G. A.; Hadjian, Armin

doi:10.1007/s13398-015-0239-1

Cited by 11 publications

(5 citation statements)

References 25 publications

(19 reference statements)

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“…which is impossible. Therefore, m = 0, and so by (27) we have v n → v in X. This concludes the proof.…”

supporting

confidence: 55%

“…In [10], Ferrara-Molica Bisci provided the existence of at least one nontrivial weak solution to a nonlinear elliptic equation with two real parameters. Inspired by this work, the authors in [27] obtained the existence of at least two distinct weak solutions; see also [26,28,39] for the existences of triple solutions. In particular, the main tools to get these existence results of multiple solutions are various critical point theorems of either Bonanno's type in [2][3][4] or Ricceri's type in [50,51].…”

mentioning

confidence: 91%

“…Stationary problems involving singular nonlinearities have garnered increasing attention because they can be corroborated as a model for many physical phenomena; see [1,8,18,43,44,48,55,57] for more details. Moreover, motivated by this large interest, singular problems have been investigated more in recent years; see [10,25,27]. In [10], Ferrara-Molica Bisci provided the existence of at least one nontrivial weak solution to a nonlinear elliptic equation with two real parameters.…”

mentioning

confidence: 99%

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Infinitely many small energy solutions to the $ p $-Laplacian problems of Kirchhoff type with Hardy potential

Kim,

Park,

Zeng

2024

DCDS-S

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The present paper is devoted to obtaining the multiplicity result of solutions to the nonlinear elliptic equations of Kirchhoff type with Hardy potential. More precisely, the main purpose of this paper, under certain assumptions on the Kirchhoff function and nonlinear term, is to show the existence of infinitely many small energy solutions to the given problem. The primary tool is the dual fountain theorem to obtain the multiplicity result. Finally, by exploiting the dual fountain theorem and the modified functional method, we demonstrate that our problem has a sequence of infinitely many weak solutions, which converges to 0 in L ∞ -space.

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“…which is impossible. Therefore, m = 0, and so by (27) we have v n → v in X. This concludes the proof.…”

supporting

confidence: 55%

mentioning

confidence: 91%

mentioning

confidence: 99%

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Infinitely many small energy solutions to the $ p $-Laplacian problems of Kirchhoff type with Hardy potential

Kim,

Park,

Zeng

2024

DCDS-S

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“…for u ∈ X. By the compact embedding X → L 1 (Ω), X → L q (Ω) there exist C 1 , C q > 0 and by (1), (10), (13) and (14)…”

Section: Two Weak Solutionsmentioning

confidence: 99%

Solutions for a singular elliptic problem involving the p(x)-Laplacian

Mahdavi¹,

Razani²

2018

Filomat

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“…In the local setting (s = 1), M. Khodabakhshi and al. [18] studied the existence of solutions to the problem (1.2) which was motivated by the work of Ferrara and Bisci [13]. They studied the existence of at least one nontrivial solution of the following elliptic problem…”

Section: Introductionmentioning

confidence: 99%

Existence results for singular elliptic problem involving a fractional p-Laplacian

Achour¹,

Bensid²

2022

Preprint

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In this article, the problems to be studied are the followingwhere Ω is a bounded regular domain in R N (N ≥ 2) containing the origin, p > 1, s ∈ (0, 1), (N > ps), λ > 0, f : Ω × R −→ R is a Carathéodory function satisfying a suitable growth condition and (−∆) s p is the fractional p-Laplacian defined aswhere B ε (x) is the open ε-ball of centre x and radius ε. Using the critical point theory combining to the fractional Hardy inequality, we show that the problem (P + ) admits at least two distinct nontrivial weak solutions. For the problem (P − ), we use the concentrationcompactness principle for fractional Sobolev spaces to give a weak lower semicontinuity result and prove that problem (P − ) admits at least one non-trivial weak solution.

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Existence of two weak solutions for some singular elliptic problems

Cited by 11 publications

References 25 publications

Infinitely many small energy solutions to the $ p $-Laplacian problems of Kirchhoff type with Hardy potential

Infinitely many small energy solutions to the $ p $-Laplacian problems of Kirchhoff type with Hardy potential

Solutions for a singular elliptic problem involving the p(x)-Laplacian

Existence results for singular elliptic problem involving a fractional p-Laplacian

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