Results 11 to 20 of about 13,793 (165)

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
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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 ( ( p , 2 ) \left ( p,2\right ) -equation), with a Carathéodory ( p − 1 ) \left ( p-1\right ) -(sub-)linear reaction.
Aizicovici, S., Papageorgiou, N. S., Staicu, V.   +2 more
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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

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
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Nodal Stabilization of the Flow in a Network with a Cycle

Journal of Optimization, Differential Equations and Their Applications, 2021
In this paper we discuss an approach to the stability analysis for classical solutions of closed loop systems that is based upon the tracing of the evolution of the Riemann invariants along the characteristics.
Martin Gugat, Sven Weiland
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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
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Nodal solutions for some singularly perturbed Dirichlet problems [PDF]

Transactions of the American Mathematical Society, 2011
Summary: We consider the equation \( -\varepsilon^2 \Delta u+u=f(u)\) in a bounded, smooth domain \( \Omega \subset \mathbb R^N\) with homogeneous Dirichlet boundary conditions. We prove the existence of nodal solutions with multiple peaks concentrating at different points of \( \Omega\).
Teresa D'Aprile, PISTOIA, Angela
openaire   +3 more sources

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
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Nodal line structure of least energy nodal solutions for Lane–Emden problems

Comptes Rendus. Mathématique, 2009
In this Note, we consider the Lane–Emden problem −Δu=λ2|u|p−2u with Dirichlet boundary conditions, where the domain Ω is an open bounded subset of R2, λ2 is the second eigenvalue of −Δ, and p>2. We prove that, if Ω is C2 and convex, the nodal line intersects ∂Ω when p is close to 2. In contrast, we also exhibit a connected — but not simply connected
Grumiau, Christopher, Troestler, Christophe   +1 more
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Multi-bump type nodal solutions having a prescribed number of nodal domains: II

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2005
This paper is a sequel to [Liu and Wang, preprint] in which we studied nodal property of multi-bump type sign-changing solutions constructed by Coti Zelati and Rabinowitz [Comm. Pure Appl. Math. 45 (1992) 1217]. In this paper we remove a technical condition that the nonlinearity is odd, which was used in [Comm. Pure Appl. Math.
Liu, Zhaoli, Wang, Zhi-Qiang
openaire   +3 more sources