Results 61 to 70 of about 446 (156)

Existence of Multiple Solutions for Certain Quasilinear Elliptic Problems Under Flux Boundary Conditions

Journal of Mathematics, Volume 2024, Issue 1, 2024.
In this paper, we consider the following quasilinear p⟶⋅‐elliptic problems with flux boundary conditions of the type −∑i=1N∂/∂xiaix,∂u/∂xi+bxupMx−2u=f1x,u−sgnug1x in Ω,∑i=1Naix,∂u/∂xiνi=cxuqx−2u+f2x,u−sgnug2x on ∂Ω.. Using the Fountain theorem and dual Fountain theorem, we prove the existence and multiplicity of solutions for a given problem, subject ...
Ahmed Ahmed, Taghi Ahmedatt, Yongqiang Fu   +2 more
wiley   +1 more source

On the critical Choquard-Kirchhoff problem on the Heisenberg group

Advances in Nonlinear Analysis, 2022
In this paper, we deal with the following critical Choquard-Kirchhoff problem on the Heisenberg group of the form: M(‖u‖2)(−ΔHu+V(ξ)u)=∫HN∣u(η)∣Qλ∗∣η−1ξ∣λdη∣u∣Qλ∗−2u+μf(ξ,u),M\left(\Vert u{\Vert }^{2})\left(-{\Delta }_{{\mathbb{H}}}u\left+V\left(\xi )u)=\
Sun Xueqi, Song Yueqiang, Liang Sihua
doaj   +1 more source

Nonlinear Choquard equations: Doubly critical case

Applied Mathematics Letters, 2018
Consider nonlinear Choquard equations \begin{equation*} \left\{\begin{array}{rcl} -Δu +u & = &(I_α*F(u))F'(u) \quad \text{in } \mathbb{R}^N, \\ \lim_{x \to \infty}u(x) & = &0, \end{array}\right. \end{equation*} where $I_α$ denotes Riesz potential and $α\in (0, N)$. In this paper, we show that when $F$ is doubly critical, i.e.
openaire   +3 more sources

Semi-classical states for the Choquard equation [PDF]

Calculus of Variations and Partial Differential Equations, 2014
28 pages, updated ...
Moroz, Vitaly, van Schaftingen, Jean
openaire   +4 more sources

Semiclassical ground state solutions for a Choquard type equation in

, 2018
In this paper we study a nonlocal singularly perturbed Choquard type equation $$-\varepsilon^2\Delta u +V(x)u =\vr^{\mu-2}\left[\frac{1}{|x|^{\mu}}\ast \big(P(x)G(u)\big)\right]P(x)g(u)$
Minbo Yang
core   +1 more source

Orbital stability of generalized Choquard equation [PDF]

Boundary Value Problems, 2016
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Xing, Sun, Xiaomei, Lv, Wenhua
openaire   +2 more sources

Normalized solutions for the Choquard equation with potential and combined nonlinearities

Advances in Nonlinear Analysis
In this paper, we study multiple normalized solutions for the following Choquard equation:
Xing Wenjun, Suo Hongmin, Lei Chunyu
doaj   +1 more source

Global dynamics of the parabolic Choquard equation with asymptotically linear nonlinearity

Journal of Inequalities and Applications
This article investigates the global dynamics of the semilinear parabolic Choquard equation ∂ t u ( x , t ) − Δ u ( x , t ) + u ( x , t ) = ( I α ∗ | u ( ⋅ , t ) | p ) ( x ) | u ( x , t ) | p − 2 u ( x , t ) + f ( u ( x , t ) ) , ( x , t ) ∈ R N × ( 0 , ∞
Salah Boulaaras
doaj   +1 more source

Nonlocal perturbations of the fractional Choquard equation

Advances in Nonlinear Analysis, 2017
We study the ...
Singh Gurpreet
doaj   +1 more source

Choquard equations with recurrent potentials

Advances in Nonlinear Analysis
Abstract In this article, we are concerned with the existence of nontrivial solutions to the Choquard equation − Δ u + α
Ding, Hui-Sheng, Liu, Quan, Long, Wei, Zhong, Lan   +3 more
openaire   +3 more sources