Results 131 to 140 of about 14,364 (164)

Nodal Solutions for Indefinite Robin Problems

Bulletin of the Malaysian Mathematical Sciences Society, 2017
Given a bounded domain \(\Omega \subseteq \mathbb{R}^N\) with a \(C^2\)-boundary, the authors study semilinear Robin problems of the form \[ \begin{cases} -\Delta u(z)+\xi(z)u(z) = f(z,u(z)) &\text{in }\Omega,\\ \frac{\partial u}{\partial n}+\beta(z)u=0 &\text{on }\partial \Omega, \end{cases} \] where the potential function \(\xi\) belongs to \(L^s ...
Filippakis, Michael, Papageorgiou, Nikolaos S.   +1 more
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Nodal solutions of a p-Laplacian equation

Proceedings of the London Mathematical Society, 2005
Summary: We prove that the \(p\)-Laplacian problem \(-\Delta_p u = f(x, u)\), with \(u \in W_0^{1,p}(\Omega)\) on a bounded domain \(\Omega \subset \mathbb R^N\), with \(p > 1\) arbitrary, has a nodal solution provided that \(f : \Omega\times\mathbb R \to \mathbb R\) is subcritical, and \(f(x, t) / |t|^{p-2}\) is superlinear.
Bartsch, Thomas, Liu, Zhaoli, Weth, Tobias   +2 more
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Nodal solutions of -Laplacian equations

Nonlinear Analysis: Theory, Methods & Applications, 2007
The aim of this paper is to study the existence of nodal radial solutions for the \(p(x)\)-Laplacian equation of the form \[ \begin{gathered} -\text{div}(|\nabla |^{p(x)-2}\nabla u)+ a(x)|u|^{p(x)-2} u=|u|^{q(x)- 2} u\quad\text{in }\Omega,\\ u\in W^{1,p(x)}_0(\Omega).\end{gathered}\tag{1} \] Using a variational method, the authors prove that, for any ...
Fan, Xianling, Zhao, Yuanzhang
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Nodal solutions for anisotropic \((p, q)\)-equations

Nonlinear Analysis: Real World Applications, 2022
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Zeng, Shengda, Papageorgiou, Nikolaos S.
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Nonexistence of nodal solutions of nonlinear elliptic equations

Nonlinear Analysis: Theory, Methods & Applications, 2001
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Bae, Soohyun, Pahk, Dae Hyeon
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ON NODAL SOLUTIONS OF THE NONLINEAR SCHRÖDINGER–POISSON EQUATIONS

Communications in Contemporary Mathematics, 2012
In this paper, we are interested in nodal solutions of nonlinear Schrödinger–Poisson equations. In particular, for a given natural number k we construct a radial solution changing sign exactly k-times.
Kim, Seunghyeok, Seok, Jinmyoung
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Nodal sets of solutions of parabolic equations: II

Communications on Pure and Applied Mathematics, 1994
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Han, Qing, Lin, Fang Hua
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Localized Nodal Solutions for System of Critical Choquard Equations

Communications in Nonlinear Science and Numerical Simulation, 2023
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A solution of the inverse nodal problem

Inverse Problems, 1997
The author considers the Sturm-Liouville problem \[ - y''+q(x)y=\lambda y, \qquad y(0)\cos\alpha+ y'(0)\sin\alpha=0, \quad y(1)\cos\beta+ y'(1)\sin\beta=0 \] and demonstrates how the potential function \(q(x)\) can be determined from observable eigenfunction nodes when either \(\alpha\) or \(\beta=0\) but not both. This extends work by \textit{O.
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Nodal solutions for nonlinear eigenvalue problems

Nonlinear Analysis, 2004
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Ma, R., Thompson, B.
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