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Cheng, Kun; Gao, Qi

doi:10.1016/s0252-9602(18)30841-5

Cited by 25 publications

(19 citation statements)

References 40 publications

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“…Remark 1.3. We point out that the results of this paper complement previous works 9,14,15,19 in the sense that we prove the existence of sign-change solutions and Cheng and Gao 29 in the sense that we consider exponential growth on the nonlinearity. Furthermore, our results extend for the fractional Laplacian some of the results contained in previous studies.…”

Section: Introduction and Main Resultssupporting

confidence: 79%

“…In order to overcome these difficulties, we define the following constrained set:

N_{n o d} = {u \in X : u^{\pm} \neq 0 and I^{'} (u) u^{\pm} = 0}

and consider a minimization problem of

I

{scriptN}_{n o d}

. Borrowing ideas from Cheng and Gao, we prove

{scriptN}_{n o d} \neq \emptyset

via modified Miranda's theorem (see Lemmas and ). Combining the ideas developed in previous studies, we prove that the minimizer of the constrained problem is also a sign‐changing solution via the quantitative deformation lemma and degree theory (see Section ).…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

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Nodal solutions for fractional elliptic equations involving exponential critical growth

Souza

Severo

Rêgo

2020

Math Methods in App Sciences

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In the present paper, we study the existence of least energy nodal solution for a Dirichlet problem driven by the 12−Laplacian operator of the following type: false(−normalΔfalse)12u+Vfalse(xfalse)u=ffalse(ufalse)0.3em0.3emin0.3emfalse(a,bfalse),u=00.3em0.3emin.5emdouble-struckR∖false(a,bfalse), where V:false[a,bfalse]→false[0,+∞false) is a continuous potential and ffalse(tfalse) is a nonlinearity that grows like expfalse(t2false) as t→+∞. By using the constraint variational method and quantitative deformation lemma, we obtain a least energy nodal solution u for the given problem. Moreover, we show that the energy of u is strictly larger than twice the ground state energy.

show abstract

Section: Introduction and Main Resultssupporting

confidence: 79%

“…In order to overcome these difficulties, we define the following constrained set:

N_{n o d} = {u \in X : u^{\pm} \neq 0 and I^{'} (u) u^{\pm} = 0}

and consider a minimization problem of

I

{scriptN}_{n o d}

. Borrowing ideas from Cheng and Gao, we prove

{scriptN}_{n o d} \neq \emptyset

Section: Introduction and Main Resultsmentioning

confidence: 99%

Nodal solutions for fractional elliptic equations involving exponential critical growth

Souza

Severo

Rêgo

2020

Math Methods in App Sciences

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show abstract

“…In this spirit, we study the existence of weak solutions for problem (1). For more details about problems related to it see for example [4], [6], [23], [24]. To the best of our knowledge, the literature for fractional Laplacian equations is still expanding and rather young.…”

Section: Introductionmentioning

confidence: 99%

Existence and multiplicity of solutions for a fractional $p$-Laplacian problem of Kirchhoff type via Krasnoselskii's genus

Benhamida¹,

Moussaoui²

2017

Math.Boh.

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We use the genus theory to prove the existence and multiplicity of solutions for the fractional p-Kirchhoff problem    − M Q |u(x) − u(y)| p |x − y| N +ps dx dy p−1 (−∆) s p u = λh(x, u) in Ω, u = 0 on R N \ Ω, where Ω is an open bounded smooth domain of R N , p > 1, N > ps with s ∈ (0, 1) fixed, Q = R 2N \ (CΩ × CΩ), λ > 0 is a numerical parameter, M and h are continuous functions.

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“…On the other hand, a great attention has recently been given to the so called fractional Kirchhoff equation (see [4,5,13] with Ω ⊂ R N being a bounded domain or Ω = R N . Problem (1.4) is related to the stationary analogue of the fractional Kirchhoff equation…”

mentioning

confidence: 99%

Ground state and nodal solutions for fractional Schrödinger-Maxwell-Kirchhoff systems with pure critical growth nonlinearity

Liu¹,

Zhang²

2021

Communications on Pure &Amp; Applied Analysis

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Sign-changing solutions for the stationary Kirchhoff problems involving the fractional Laplacian inRN

Cited by 25 publications

References 40 publications

Nodal solutions for fractional elliptic equations involving exponential critical growth

Nodal solutions for fractional elliptic equations involving exponential critical growth

Existence and multiplicity of solutions for a fractional $p$-Laplacian problem of Kirchhoff type via Krasnoselskii's genus

Ground state and nodal solutions for fractional Schrödinger-Maxwell-Kirchhoff systems with pure critical growth nonlinearity

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