Results 1 to 10 of about 44,643 (219)

Infinite number of solutions for some elliptic eigenvalue problems of Kirchhoff-type with non-homogeneous material

Boundary Value Problems, 2021
In this paper, using variational method, we study the existence of an infinite number of solutions (some are positive, some are negative, and others are sign-changing) for a non-homogeneous elliptic Kirchhoff equation with a nonlinear reaction term.
Baoqiang Yan, Donal O’Regan, Ravi P. Agarwal   +2 more
doaj   +1 more source

A Kirchhoff-type problem involving concave-convex nonlinearities

Advances in Difference Equations, 2021
A Kirchhoff-type problem with concave-convex nonlinearities is studied. By constrained variational methods on a Nehari manifold, we prove that this problem has a sign-changing solution with least energy.
Yuan Gao, Lishan Liu, Shixia Luan, Yonghong Wu   +3 more
doaj   +1 more source

Ground state sign-changing solutions for critical Choquard equations with steep well potential

Electronic Journal of Qualitative Theory of Differential Equations, 2022
In this paper, we study sign-changing solution of the Choquard type equation \begin{align*} -\Delta u+\left(\lambda V(x)+1\right)u =\big(I_\alpha\ast|u|^{2_\alpha^*}\big)|u|^{2_\alpha^*-2}u +\mu|u|^{p-2}u\quad \mbox{in}\ \mathbb{R}^N, \end{align*} where
Yong-Yong Li, Gui-Dong Li, Chun-Lei Tang
doaj   +1 more source

Least-energy sign-changing solutions for Kirchhoff–Schrödinger–Poisson systems in R3 $\mathbb{R}^{3}$

Boundary Value Problems, 2019
In this paper, we study the following Kirchhoff–Schrödinger–Poisson systems: {−(a+b∫R3|∇u|2dx)Δu+V(x)u+ϕu=f(u),x∈R3,−Δϕ=u2,x∈R3, $$\textstyle\begin{cases} -(a+b\int _{\mathbb{R}^{3}} \vert \nabla u \vert ^{2}\,dx)\Delta u+V(x)u+\phi u=f(u), &x \in ...
Da-Bin Wang, Tian-Jun Li, Xinan Hao
doaj   +1 more source

Existence of sign-changing solution with least energy for a class of Kirchhoff-type equation in $\mathbb{R}^N$

Electronic Journal of Qualitative Theory of Differential Equations, 2017
We consider the existence of least energy sign-changing (nodal) solution of Kirchhoff-type elliptic problems with general nonlinearity. Using a truncated technique and constrained minimization on the nodal Nehari manifold, we obtain that the Kirchhoff ...
Xianzhong Yao, Chunlai Mu
doaj   +1 more source

Sign-changing solutions for Schrödinger–Kirchhoff-type fourth-order equation with potential vanishing at infinity

Journal of Inequalities and Applications, 2021
The purpose of this paper is to study the existence of sign-changing solution to the following fourth-order equation: 0.1 Δ 2 u − ( a + b ∫ R N | ∇ u | 2 d x ) Δ u + V ( x ) u = K ( x ) f ( u ) in  R N , $$ \Delta ^{2}u- \biggl(a+ b \int _{\mathbb{R}^{N}}
Wen Guan, Hua-Bo Zhang
doaj   +1 more source

Ground state sign-changing solutions for Kirchhoff equations with logarithmic nonlinearity

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper, we study Kirchhoff equations with logarithmic nonlinearity: \begin{equation*} \begin{cases} -(a+b\int_\Omega|\nabla u|^2)\Delta u+ V(x)u=|u|^{p-2}u\ln u^2, & \mbox{in}\ \Omega,\\ u=0,& \mbox{on}\ \partial\Omega, \end{cases} \end{equation*}
Lixi Wen, Xianhua Tang, Sitong Chen
doaj   +1 more source

On a sign-changing solution for some fractional differential equations

Boundary Value Problems, 2017
In this paper, a kind of αth ( 3 < α ≤ 4 ...
Kemei Zhang
doaj   +1 more source

Sobolev norm estimates of solutions for the sublinear Emden-Fowler equation [PDF]

Opuscula Mathematica, 2013
We study the sublinear Emden-Fowler equation in small domains. As the domain becomes smaller, so does any solution. We investigate the convergence rate of the Sobolev norm of solutions as the volume of the domain converges to zero. The result is obtained
Ryuji Kajikiya
doaj   +1 more source

Nodal solution for critical Kirchhoff-type equation with fast increasing weight in R 2 $\mathbb{R}^{2}$

Journal of Inequalities and Applications, 2023
In this paper, we investigate the existence of a least-energy sign-changing solutions for the following Kirchhoff-type equation: − ( 1 + b ∫ R 2 K ( x ) | ∇ u | 2 d x ) div ( K ( x ) ∇ u ) = K ( x ) f ( u ) , x ∈ R 2 , $$ - \biggl(1+b \int _{\mathbb{R ...
Qin Qin, Guo Jie, Hongmin Suo
doaj   +1 more source