Results 231 to 240 of about 91,659 (256)

Existence and multiplicity of solutions for Schrödinger–Poisson equations with sign-changing potential

Calculus of Variations and Partial Differential Equations, 2014
The authors study existence, multiplicity and concentration of solutions to the nonlinear Schrödinger-Poisson equations \[ \begin{alignedat}{2} - \Delta u + \lambda V(x) u + K(x) \varphi(x) u & = f(x,u) & \quad & \text{in } \mathbb{R}^3, \\ - \Delta \varphi & = K(x) u^2 & \quad & \text{in } \mathbb{R}^3,\end{alignedat} \] under various assumptions on ...
Ye, Yiwei, Tang, Chun-Lei
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Multiple solutions for the Schrödinger equations with sign-changing potential and Hartree nonlinearity

Applied Mathematics Letters, 2018
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Guofeng Che, Haibo Chen 0007
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Bound states for semilinear Schrödinger equations with sign-changing potential

Calculus of Variations and Partial Differential Equations, 2007
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Ding, Yanheng, Szulkin, Andrzej
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Infinitely Many Sign‐Changing Solutions for a Schrödinger Equation With Competing Potentials

Mathematical Methods in the Applied Sciences
ABSTRACTConsider the following nonlinear problem with competing potentials: , where , and are positive functions. We construct infinitely many nonradial sign‐changing solutions to the equation above by the Lyapunov–Schmidt reduction method.
Ke Wu, Kaijing Cheng, Fen Zhou
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Sign-changing solutions for a critical exponential problem with competing potentials

Topological Methods in Nonlinear Analysis
We establish the existence, concentration, and exponential decay of a family of sign-changing solutions for a problem involving exponential critical growth, described by the equation: $$ \begin{cases} -\epsilon^{2}\mbox{div}\left(a(x)\nabla u\right)+V(x)u =K(x) f(u) & \mbox{in $\mathbb{R}^2,$}\\ u \in H^{1}\big(\mathbb{R}^{2}\big).
Willy Barahona, Eugenio Cabanillas Lapa, Giovany M. Figueiredo   +2 more
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Sign-Changing Solutions for a Fractional Schrödinger Equation with Vanishing Potential

2020
In this chapter we study the existence of least energy sign-changing (or nodal) solutions for the following nonlinear problem involving the fractional Laplacian: $$\displaystyle \left \{ \begin {array}{ll} (-\Delta )^{s} u + V(x)u = K(x) f(u) &\mbox{ in } \mathbb {R}^{N}, \\ u\in \mathcal {D}^{s, 2}(\mathbb {R}^{N}), \end {array} \right ...
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The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions

Journal of Differential Equations, 2011
Yueh-Cheng Kuo, Tsung-Fang Wu
exaly  

Sign-changing solutions for a class of Kirchhoff-type problem in bounded domains

Journal of Differential Equations, 2015
Wei Shuai
exaly  

A note on the sign-changing solutions to elliptic problems with critical Sobolev and Hardy terms

Journal of Differential Equations, 2003
Daomin Cao, Shuangjie Peng
exaly  

Existence and concentration of sign-changing solutions to Kirchhoff-type system with Hartree-type nonlinearity

Journal of Mathematical Analysis and Applications, 2017
Fuyi Li
exaly