Results 1 to 10 of about 2,960,114 (284)

Infinitely many nodal solutions for a class of quasilinear elliptic equations

Electronic Journal of Qualitative Theory of Differential Equations, 2021
In this paper, we study the existence of infinitely many nodal solutions for the following quasilinear elliptic equation \begin{equation*} \begin{cases} -\nabla\cdot\left[\phi'(|\nabla u|^2)\nabla u\right]+|u|^{\alpha-2}u=f(u) , \quad x\in \mathbb{R}^N,\\
Xiaolong Yang
doaj   +1 more source

Localized nodal solutions for semiclassical nonlinear Kirchhoff equations

Electronic Journal of Differential Equations, 2022
In this article, we consider the existence of localized sign-changing solutions for the semiclassical Kirchhoff equation  $$ -(\varepsilon^2a+\varepsilon b\int_{\mathbb{R}^3}|\nabla u|^2dx) \Delta u+V(x)u =|u|^{p-2}u, \quad x\in \mathbb{R}^3,\; u\in H^1(
Lixia Wang
doaj   +3 more sources

Approximate nonradial solutions for the Lane-Emden problem in the ball

Advances in Nonlinear Analysis, 2021
In this paper we provide a numerical approximation of bifurcation branches from nodal radial solutions of the Lane Emden Dirichlet problem in the unit ball in ℝ2, as the exponent of the nonlinearity varies.
Fazekas Borbála, Pacella Filomena, Plum Michael   +2 more
doaj   +1 more source

Investigation of the modular building metal frame nodal connection rotational stiffness [PDF]

E3S Web of Conferences, 2021
The research subject is the rotational stiffness of the modular building metal frame nodal connection. The stiffness of nodal connections has a significant impact on the results of calculating the load-bearing frame of a modular building.
Shirokov Vyacheslav, Veremeenko Oleg, Alpatov Vadim   +2 more
doaj   +1 more source

Resonant Anisotropic (p,q)-Equations

Mathematics, 2020
We consider an anisotropic Dirichlet problem which is driven by the (p(z),q(z))-Laplacian (that is, the sum of a p(z)-Laplacian and a q(z)-Laplacian), The reaction (source) term, is a Carathéodory function which asymptotically as x±∞ can be resonant with
Leszek Gasiński, Nikolaos S. Papageorgiou   +1 more
doaj   +1 more source

Linear Sturm-Liouville problems with Riemann-Stieltjes integral boundary conditions [PDF]

Opuscula Mathematica, 2018
We study second-order linear Sturm-Liouville problems involving general homogeneous linear Riemann-Stieltjes integral boundary conditions. Conditions are obtained for the existence of a sequence of positive eigenvalues with consecutive zero counts of the
Qingkai Kong, Thomas E. St. George
doaj   +1 more source

On sign-changing solutions for (p,q)-Laplace equations with two parameters

Advances in Nonlinear Analysis, 2016
We investigate the existence of nodal (sign-changing) solutions to the Dirichlet problem for a two-parametric family of partially homogeneous (p,q){(p,q)}-Laplace equations -Δp⁢u-Δq⁢u=α⁢|u|p-2⁢u+β⁢|u|q-2⁢u{-\Delta_{p}u-\Delta_{q}u=\alpha\lvert u\rvert^{p-
Bobkov Vladimir, Tanaka Mieko
doaj   +1 more source

Nodal solutions with a prescribed number of nodes for the Kirchhoff-type problem with an asymptotically cubic term

Advances in Nonlinear Analysis, 2023
In this article, we study the following Kirchhoff equation: (0.1)−(a+b‖∇u‖L2(R3)2)Δu+V(∣x∣)u=f(u)inR3,-(a+b\Vert \nabla u{\Vert }_{{L}^{2}\left({{\mathbb{R}}}^{3})}^{2})\Delta u+V\left(| x| )u=f\left(u)\hspace{1.0em}\hspace{0.1em}\text{in}\hspace{0.1em ...
Wang Tao, Yang Yanling, Guo Hui
doaj   +1 more source

Multiple nodal solutions of the Kirchhoff-type problem with a cubic term

Advances in Nonlinear Analysis, 2022
In this article, we are interested in the following Kirchhoff-type problem (0.1)−a+b∫RN∣∇u∣2dxΔu+V(∣x∣)u=∣u∣2uinRN,u∈H1(RN),\left\{\begin{array}{l}-\left(a+b\mathop{\displaystyle \int }\limits_{{{\mathbb{R}}}^{N}}| \nabla u\hspace{-0.25em}{| }^{2}{\rm{d}}
Wang Tao, Yang Yanling, Guo Hui
doaj   +1 more source

Localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth

Electronic Journal of Differential Equations, 2022
In this article, we study the existence of localized nodal solutions for semiclassical quasilinear Choquard equations with subcritical growth $$-\varepsilon^p \Delta_{p} v +V(x)|v|^{p-2}v = \varepsilon^{\alpha-N} |v|^{q-2}v \int_{\mathbb{R}^N} \frac{|v ...
Bo Zhang, Xiangqing Liu
doaj   +3 more sources