Results 21 to 30 of about 1,278 (268)
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
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Variational Arbitrary Lagrangian-Eulerian Method [PDF]
, 2003 This thesis is concerned with the development of Variational Arbitrary Lagrangian-Eulerian method (VALE) method. VALE is essentially finite element method generalized to account for horizontal variations, in particular, variations in nodal coordinates ...
Thoutireddy, Pururav
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Boundary Value Problems, 2019 This paper is concerned with the existence of a sign-changing solution to a class of quasilinear Schrödinger–Poisson systems. There are some technical difficulties in applying variational methods directly to the problem because the quasilinear term makes
Lizhen Chen, Xiaojing Feng, Xinan Hao
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Variational Nodal Method for Solving P1 Equation
Yuanzineng kexue jishuStarting from the neutron transport equation, the diffusion equation is firstly derived via the P1 approximation, and subsequently the neutron diffusion equation is obtained through the diffusion approximation.
LI Yisong, LI Yunzhao, FAN Yuwen, QIN Junwei, WANG Songzhe
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Sign-Changing Solutions for Nonlinear Elliptic Problems Depending on Parameters
International Journal of Differential Equations, 2010 The study of multiple solutions for quasilinear elliptic problems under Dirichlet or nonlinear Neumann type boundary conditions has received much attention over the last decades.
Siegfried Carl, Dumitru Motreanu
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Indiana University Mathematics Journal, 2022 Summary: In this work we use two different methods to get nodal solutions to quasilinear elliptic problems involving the \(1\)-Laplacian operator. In the first one, we develop an approach based on a minimization of the energy functional associated with a problem involving the \(1\)-Laplacian operator in \(\mathbb{R}^N\), on a subset of the Nehari set ...
Figueiredo, Giovany M. +1 more
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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
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Least energy sign-changing solutions for Kirchhoff–Poisson systems
Boundary Value Problems, 2019 The paper deals with the following Kirchhoff–Poisson systems: 0.1 {−(1+b∫R3|∇u|2dx)Δu+u+k(x)ϕu+λ|u|p−2u=h(x)|u|q−2u,x∈R3,−Δϕ=k(x)u2,x∈R3, $$ \textstyle\begin{cases} - ( {1+b\int _{{\mathbb{R}}^{3}} { \vert \nabla u \vert ^{2}\,dx} } ) \Delta u+u+k(x)\phi
Guoqing Chai, Weiming Liu
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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 +1 more
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Stabilized conforming nodal integration: Exactness and variational justification [PDF]
, 2004 In most Galerkin mesh-free methods, background integration cells partitioning the problem domain are required to evaluate the weak form. It is therefore worthwhile to consider these methods using the notions of domain decomposition with the integration ...
X. H. Liu +7 more
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