Liouville type theorem for stable solutions of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml1" display="inline" overflow="scroll" altimg="si1.gif"><mml:mi>p</mml:mi></mml:math>-Laplace equation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="mml2" display="inline" overflow="scroll" altimg="si2.gif"><mml:msup><mml:mrow><mml:mi mathvariant="double-struck">R</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:msup></mml:math>

Chen, Caisheng

doi:10.1016/j.aml.2016.11.014

Cited by 16 publications

(20 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…If p =2, b =0, θ >−2, then μ 0 (2,0, θ )=10+4 θ , which equals to the critical exponent q c in Wang and Ye . If b =0, θ >− p , then

μ_{0} false(p, 0, θ false) = \frac{p false(p + 3 false) + 4 θ}{p - 1},

which equals to the critical exponent μ 0 ( p , a ) in Chen et al If γ =0, Theorem recovers the previous results for the p ‐Laplace operator in Le, theorem 1.5 and Le et al, theorem 1.4…”

Section: Introductionsupporting

confidence: 80%

“…However, as far as we know, the Liouville‐type theorem for the problem of with γ ≠0, p >2 and a ( z ), h ( z )≢1 has not been studied in the literature. Motivated by the above and the idea of other studies, in this paper, we are devoted to establish the Liouville property for the stable weak solutions of class

W_{normall o c}^{1, p}

to Equation.…”

Section: Introductionmentioning

confidence: 99%

“…Obviously, when γ =0, Equation becomes p ‐Laplace problem with the weighted power nonlinearity. So far, there have been many works dealing with the stable solutions of with γ =0 (see previous works and the references therein). The pioneering work in this direction is due to Farina; he proved that −△ u = e u has no stable classical solutions in

R^{N}

for 2 ≤ N ≤ 9.…”

Section: Introductionmentioning

confidence: 99%

“…Later, in the same year, Wang and Ye deal with more specific equation −△ u =| x | b e u but for stable solutions of class of

H_{normall o c}^{1}

which covers solutions having singularities. After that, the result in Wang and Ye was extended to problem with f ( u )= e u in Huang et al and equation −△ p u = f ( x ) g ( u ) in Chen et al, where g ( u )= e u or g ( u )=− u − q . Similar works on singular problems can be founded in other studies …”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Liouville‐type theorem for nonlinear elliptic equations involving p‐Laplace–type Grushin operators

Wei

Chen

et al. 2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…If p =2, b =0, θ >−2, then μ 0 (2,0, θ )=10+4 θ , which equals to the critical exponent q c in Wang and Ye . If b =0, θ >− p , then

μ_{0} false(p, 0, θ false) = \frac{p false(p + 3 false) + 4 θ}{p - 1},

which equals to the critical exponent μ 0 ( p , a ) in Chen et al If γ =0, Theorem recovers the previous results for the p ‐Laplace operator in Le, theorem 1.5 and Le et al, theorem 1.4…”

Section: Introductionsupporting

confidence: 80%

W_{normall o c}^{1, p}

to Equation.…”

Section: Introductionmentioning

confidence: 99%

R^{N}

for 2 ≤ N ≤ 9.…”

Section: Introductionmentioning

confidence: 99%

“…Later, in the same year, Wang and Ye deal with more specific equation −△ u =| x | b e u but for stable solutions of class of

H_{normall o c}^{1}

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Liouville‐type theorem for nonlinear elliptic equations involving p‐Laplace–type Grushin operators

Wei

Chen

et al. 2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

show abstract

“…Proof of Proposition Our proof is inspired by the techniques used in , but we need to pay more attention with

W_{l o c}^{1, p}

solution. As u is not assumed to be bounded,

e^{β u} ψ

is not, a priori, a suitable test function for any

β > 0

, even with

ψ \in C_{c}^{\infty} false(normalΩ false)

.…”

Section: Liouville Type Theoremmentioning

confidence: 99%

Low dimensional instability for quasilinear problems of weighted exponential nonlinearity

2018

Mathematische Nachrichten

View full text Add to dashboard Cite

We prove a sharp Liouville type theorem for stable Wloc1,p solutions of the equation −normalΔpu=ffalse(xfalse)euon the entire Euclidean space RN, where p>2 and f is a continuous and nonnegative function in double-struckRN∖false{0false} such that ffalse(xfalse)≥a|x|q as false|xfalse|≥R0>0, where q>−p and a>0. Our theorem holds true for 0false2≤N<0falsep2+3p+4qp−1 and is sharp in the case ffalse(xfalse)=a|x|q.

show abstract

Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter

Wei

Yang

et al. 2021

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we study the following quasilinear Schrödinger equations −Δu−Δ(|u|2α)|u|2α−2u=ω(x)|u|q−1u,x∈ℝN, where α>12 is a parameter, q>3α−1+α2α, ωfalse(xfalse)∈Cfalse(ℝN\false{0false}false) is a positive function. We establish a Liouville type theorem for the class of stable bounded sign‐changing solutions under suitable assumptions on ω(x), q, α and N.

show abstract

Liouville type theorem for stable solutions ofp-Laplace equation inRN

Cited by 16 publications

References 10 publications

Liouville‐type theorem for nonlinear elliptic equations involving p‐Laplace–type Grushin operators

Liouville‐type theorem for nonlinear elliptic equations involving p‐Laplace–type Grushin operators

Low dimensional instability for quasilinear problems of weighted exponential nonlinearity

Stable solutions to quasilinear Schrödinger equations of Lane–Emden type with a parameter

Contact Info

Product

Resources

About