Nodal Solutions of a Perturbed Elliptic Problem
, 2008 Multiple nodal solutions are obtained for the elliptic problem -Δu = f(x, u) + εg (x, u) in Ω, u =0 on ∂Ω , where ε is a parameter, Ω is a smooth bounded domain in R^{N}, f ϵ C(overline{Ω} x R)$, g ϵ C(overline{Ω} x R). For a superlinear C^{1} function f which is odd in u and for any C^{1} function g, we prove that for any j ϵ N there exists ε _{j} > 0
Li, Yi, Liu, Z., Zhao, C.
core +7 more sources
Nodal solutions for the Choquard equation [PDF]
Journal of Functional Analysis, 2016 We consider the general Choquard equations $$ -Δu + u = (I_α\ast |u|^p) |u|^{p - 2} u $$ where $I_α$ is a Riesz potential. We construct minimal action odd solutions for $p \in (\frac{N + α}{N}, \frac{N + α}{N - 2})$ and minimal action nodal solutions for $p \in (2,\frac{N + α}{N - 2})$.
GHIMENTI, MARCO GIPO +1 more
openaire +3 more sources
Nodal solutions for (𝑝,2)-equations
Transactions of the American Mathematical Society, 2014 In this paper, we study a nonlinear elliptic equation driven by the sum of a p p -Laplacian and a Laplacian (
Aizicovici, S. +2 more
openaire +4 more sources
Nondegeneracy of Nodal Solutions to the Critical Yamabe Problem [PDF]
Communications in Mathematical Physics, 2015 The interesting paper under review deals with the critical Yamabe problem \[ -\Delta u= \dfrac{n(n-2)}{4}|u|^\frac{4}{n-2}u,\quad u\in \mathcal{D}^{1,2}(\mathbb{R}^n), \] where \(n\geq 3\) and \(\mathcal{D}^{1,2}(\mathbb{R}^n)\) is the completion of \(C^\infty_0(\mathbb{R}^n)\) with respect to the norm \(\sqrt{\int_{\mathbb{R}^n} |\nabla u|^2}\).
Musso Polla, Mónica, Wei, J.
openaire +5 more sources
Existence and Asymptotic Profile of Nodal Solutions to Supercritical Problems
Advanced Nonlinear Studies, 2017 We establish the existence of nodal solutions to the supercritical ...
Clapp Mónica, Pacella Filomena
doaj +2 more sources
Multiple nodal solutions of nonlinear Choquard equations [PDF]
Electronic Journal of Differential Equations, 2017 In this article, we consider the existence of multiple nodal solutions of the nonlinear Choquard equation $$\displaylines{ -\Delta u+u=(|x|^{-1}\ast|u|^p)|u|^{p-2}u \quad \text{in }\mathbb{R}^3,\cr u\in H^1(\mathbb{R}^3), }$$ where $p\in (5/2,5 ...
Zhihua Huang, Jianfu Yang, Weilin Yu
doaj +2 more sources
NOVEL NUMERICAL PROCEDURES FOR LIMIT ANALYSIS OF STRUCTURES: MESH-FREE METHODS AND MATHEMATICAL PROGRAMMING [PDF]
, 2010 Current research in the field of limit analysis is focussing on the development of numerical tools which are sufficiently efficient and robust to be used in engineering practice.
Le, Canh
core +7 more sources
Oddness of least energy nodal solutions on radial domains [PDF]
Electronic Journal of Differential Equations, 2010 In this article, we consider the Lane-Emden problem $$displaylines{ Delta u(x) + |{u(x)}mathclose|^{p-2}u(x)=0, quad hbox{for } xinOmega,cr u(x)=0, quad hbox{for } xinpartialOmega, }$$ where $2 < p < 2^{*}$ and $Omega$ is a ball or an annulus
Christopher Grumiau +1 more
doaj +2 more sources
Symmetry of Nodal Solutions for Singularly Perturbed Elliptic Problems on a Ball [PDF]
, 2004 In [40], it was shown that the following singularly perturbed Dirichlet problem \ep^2 \Delta u - u+ |u|^{p-1} u=0, \ \mbox{in} \ \Om,\] \[ u=0 \ \mbox{on} \ \partial \Om has a nodal solution u_\ep which has the least energy among all nodal solutions.
Winter, M +5 more
core +1 more source
Analysis of the asymmetrically expressed Ablim1 locus reveals existence of a lateral plate Nodal-independent left sided signal and an early, left-right independent role for nodal flow. [PDF]
, 2010 BACKGROUND: Vertebrates show clear asymmetry in left-right (L-R) patterning of their organs and associated vasculature. During mammalian development a cilia driven leftwards flow of liquid leads to the left-sided expression of Nodal, which in turn ...
Norris, Dominic P. +23 more
core +1 more source