Results 11 to 20 of about 2,960,114 (284)

Nodal solutions of nonlocal boundary value problems [PDF]

Mathematical Modelling and Analysis, 2009
We study the nonlinear boundary value problem consisting of the second order differential equation on [a, b] and a boundary condition involving a Riemann‐Stieltjes integral. By relating it to the eigenvalues of a linear Sturm‐Liouville problem with a two‐
John Chamberlain, Lingju Kong, Qingkai Kong   +2 more
doaj   +3 more sources

Nodal solutions of weighted indefinite problems [PDF]

Journal of Evolution Equations, 2020
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the associated high order eigenvalues might not be concave as it is the lowest one.
M. Fencl, J. López-Gómez
openaire   +6 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., Papageorgiou, N. S., Staicu, V.   +2 more
openaire   +4 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, Van Schaftingen, Jean   +1 more
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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 nonlinear Schrodinger systems

Electronic Journal of Differential Equations
In this article we consider the nonlinear Schrodinger system $$\displaylines{ - \Delta u_j + \lambda_j u_j = \sum_{i=1}^k \beta_{ij} u_i^2 u_j, \quad \hbox{in } \Omega, \cr u_j ( x ) = 0,\quad \hbox{on } \partial \Omega , \; j=1,l\dots,k , }$$ where ...
Xue Zhou, Xiangqing Liu
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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.
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Localized nodal solutions for parameter-dependent quasilinear Schrodinger equations [PDF]

Electronic Journal of Differential Equations, 2021
In this article, we apply a new variational perturbation method to study the existence of localized nodal solutions for parameter-dependent semiclassical quasilinear Schrodinger equations, under a certain parametric conditions.
Rui He, Xiangqing Liu
doaj   +4 more sources

On nodal ground states for Schrodinger systems [PDF]

Electronic Journal of Differential Equations
In this article we characterize the least energy nodal and semi-nodal solutions to some Schrodinger system as the minimum on constrained Nehari sets of codimension 4 and 3, respectively; thus allowing to compute their Morse index and the exact number ...
Anna Lisa Amadori
doaj   +4 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