Results 31 to 40 of about 341 (48)

The properties of a new fractional g-Laplacian Monge-Ampère operator and its applications

Advances in Nonlinear Analysis
In this article, we first introduce a new fractional gg-Laplacian Monge-Ampère operator: Fgsv(x)≔infP.V.∫Rngv(z)−v(x)∣C−1(z−x)∣sdz∣C−1(z−x)∣n+s∣C∈C,{F}_{g}^{s}v\left(x):= \inf \left\{\hspace{0.1em}\text{P.V.}\hspace{0.1em}\mathop{\int }\limits_{{{\mathbb{
Wang Guotao, Yang Rui, Zhang Lihong
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Sign changing solutions of Lane Emden problems with interior nodal line and semilinear heat equations

, 2013
We consider the semilinear Lane Emden problem in a smooth bounded simply connected domain in the plane, invariant by the action of a finite symmetry group G.
De Marchis, Francesca, Ianni, Isabella, Pacella, Filomena   +2 more
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Multiple solutions to a magnetic nonlinear Choquard equation

, 2011
We consider the stationary nonlinear magnetic Choquard equation [(-\mathrm{i}\nabla+A(x))^{2}u+V(x)u=(\frac{1}{|x|^{\alpha}}\ast |u|^{p}) |u|^{p-2}u,\quad x\in\mathbb{R}^{N}%] where $A\ $is a real valued vector potential, $V$ is a real valued scalar ...
A. Ambrosetti, E. Fadell, E.H. Lieb, E.H. Lieb, I.M. Moroz, J. Ginibre, J. Wei, L. Ma, M. Clapp, M. Nolasco, M. Struwe, M. Willem, M.J. Esteban, Mónica Clapp, N. Ackermann, P. Tod, P.-L. Lions, R. Palais, R. Penrose, R. Penrose, R. Penrose, S. Cingolani, S. Cingolani, S. Secchi, Silvia Cingolani, Simone Secchi, T. tom Dieck, Z. Zhang   +27 more
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Nontrivial solutions for resonance quasilinear elliptic systems

Advances in Nonlinear Analysis
We establish an Amann-Zehnder-type result for resonance systems of quasilinear elliptic equations with homogeneous Dirichlet boundary conditions, involving nonlinearities growing asymptotically (p,q)\left(p,q)-linear at infinity.
Borgia Natalino, Cingolani Silvia, Vannella Giuseppina   +2 more
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An upper bound for the least energy of a sign-changing solution to a zero mass problem

Advanced Nonlinear Studies
We give an upper bound for the least possible energy of a sign-changing solution to the nonlinear scalar field equation −Δu=f(u),u∈D1,2(RN), $-{\Delta}u=f\left(u\right), u\in {D}^{1,2}\left({\mathrm{R}}^{N}\right),$ where N ≥ 5 and the nonlinearity f is
Clapp Mónica, Maia Liliane, Pellacci Benedetta   +2 more
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Moving planes and sliding methods for fractional elliptic and parabolic equations

Advanced Nonlinear Studies
In this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions.
Chen Wenxiong, Hu Yeyao, Ma Lingwei
doaj   +1 more source

Hopf's lemma, asymptotic radial symmetry, and monotonicity of solutions to the logarithmic Laplacian parabolic system

Advances in Nonlinear Analysis
In this article, we extend the asymptotic method of moving planes to the following logarithmic Laplacian parabolic system: ∂z∂t(η,t)+(−△)ℒz(η,t)=f(t,v(η,t)),(η,t)∈B1(0)×[0,∞),∂v∂t(η,t)+(−△)ℒv(η,t)=g(t,z(η,t)),(η,t)∈B1(0)×[0,∞),z(η,t)=0,v(η,t)=0,(η,t)∈B1c(
Wang Guotao, Wang Jing
doaj   +1 more source

Qualitative properties of two-end solutions to the Allen–Cahn equation in R3 ${\mathbb{R}}^{3}$

Advanced Nonlinear Studies
A solution of the Allen–Cahn equation in R3 ${\mathbb{R}}^{3}$ is called a two-end solution if its nodal set is asymptotic to (x′,z)∈R3:z=ki⁡ln|x′|+ci,1≤i≤2 $\left\{\left({x}^{\prime },z\right)\in {\mathbb{R}}^{3}:z={k}_{i}\mathrm{ln}\vert {x}^{\prime }\
Liang Weizhao, Yang Jianmin
doaj   +1 more source

Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_ ...
Yang Zerong, He Yong
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Multidimensional entire solutions for an elliptic system modelling phase separation

, 2016
For the system of semilinear elliptic equations \[ \Delta V_i = V_i \sum_{j \neq i} V_j^2, \qquad V_i > 0 \qquad \text{in $\mathbb{R}^N$} \] we devise a new method to construct entire solutions.
Soave, Nicola, Zilio, Alessandro
core   +1 more source