Results 51 to 60 of about 1,232 (95)
On an initial‐boundary value problem for the nonlinear Schrödinger equation
International Journal of Mathematics and Mathematical Sciences, Volume 2, Issue 3, Page 503-522, 1979., 1979 We study an initial‐boundary value problem for the nonlinear Schrödinger equation, a simple mathematical model for the interaction between electromagnetic waves and a plasma layer. We prove a global existence and uniqueness theorem and establish a Galerkin method for solving numerically the problem.
Herbert Gajewski
wiley +1 more source
Global Schauder estimates for kinetic Kolmogorov-Fokker-Planck equations
Advanced Nonlinear StudiesWe present global Schauder type estimates in all variables and unique solvability results in kinetic Hölder spaces for kinetic Kolmogorov-Fokker-Planck (KFP) equations.
Dong Hongjie, Yastrzhembskiy Timur
doaj +1 more source
Solitons in gauge theories: Existence and dependence on the charge
Advances in Nonlinear Analysis, 2014 In this paper we review recent results on the existence of non-topological solitons in classical relativistic nonlinear field theories. We follow the Coleman approach, which is based on the existence of two conservation laws, energy and charge.
Bonanno Claudio
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Imbedding inequalities with Lφ-norms for composite operators
Journal of Inequalities and Applications, 2013 In this paper, we prove imbedding inequalities with Lφ-norms for the composition of the potential operator and homotopy operator applied to differential forms. We also establish the global imbedding inequality in Lφ-averaging domains.
Yuming Xing, S. Ding
semanticscholar +1 more source
, 2007 Auscher, McIntosh and Tchamitchian studied the heat kernels of second order elliptic operators in divergence form with complex bounded measurable coefficients on $\mathbb{R}^n$.
Kim, Seick
core +2 more sources
Rigidity results for some boundary quasilinear phase transitions
, 2008 We consider a quasilinear equation given in the half-space, i.e. a so called boundary reaction problem. Our concerns are a geometric Poincar\'e inequality and, as a byproduct of this inequality, a result on the symmetry of low-dimensional bounded stable ...
Sire, Yannick, Valdinoci, Enrico
core +2 more sources
An upper bound for the least energy of a sign-changing solution to a zero mass problem
Advanced Nonlinear StudiesWe 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 +2 more
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Multiplicity of normalized solutions for nonlinear Choquard equations
Advanced Nonlinear StudiesIn this paper, we consider the following nonlinear Choquard equation with prescribed L 2-norm: −Δu+λu=Iα∗F(u)f(u) in RN,∫RN|u|2dx=a>0,u∈H1(RN), $\begin{cases}-{\Delta}u+\lambda u=\left({I}_{\alpha }\ast F\left(u\right)\right)f\left(u\right) \,\text{in}\,
Long Chun-Fei +3 more
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Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations
Advances in Nonlinear Analysis, 2019 Homogenisation of global 𝓐ε and exponential 𝓜ε attractors for the damped semi-linear anisotropic wave equation ∂t2uε+y∂tuε−divaxε∇uε+f(uε)=g,$\begin{array}{} \displaystyle \partial_t ^2u^\varepsilon + y \partial_t u^\varepsilon-\operatorname{div} \left(a\
Cooper Shane, Savostianov Anton
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The interior curvature bounds for a class of curvature quotient equations
Advanced Nonlinear StudiesFor elliptic partial differential equations, the pure interior C 2 estimates and Pogorelov type estimates are important issues. In this paper, we study the interior estimates of Γk̃ $\tilde {{{\Gamma}}_{k}}$ -admissible solutions for curvature quotient ...
Jia Haohao
doaj +1 more source