Strichartz estimates for non‐degenerate Schrödinger equations
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DOI: 10.1002/mana.201800148
Abstract: We consider the Schrödinger equation with a non‐degenerate metric on the Euclidean space. We study local in time Strichartz estimates for the Schrödinger equation without loss of derivatives including the endpoint case. In contrast to… read more here.
Keywords: dinger equation; strichartz estimates; estimates non; non degenerate ... See more keywords
A note on the Schrödinger smoothing effect
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DOI: 10.1002/mana.201800502
Abstract: The Kato–Yajima smoothing estimate is a smoothing weighted L2 estimate with a singular power weight for the Schrödinger propagator. The weight has been generalized relatively recently to Morrey–Campanato weights. In this paper we make this… read more here.
Keywords: schr; note schr; dinger smoothing; schr dinger ... See more keywords
Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential
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DOI: 10.1002/mana.201900427
Abstract: We consider a class of L2‐supercritical inhomogeneous nonlinear Schrödinger equations with potential in three dimensions. In the focusing case, using a recent method of Dodson and Murphy, we first study the energy scattering below the… read more here.
Keywords: class; equations potential; nonlinear schr; inhomogeneous nonlinear ... See more keywords
Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction
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DOI: 10.1002/mana.202400068
Abstract: In this work, we study the existence of various classes of standing waves for a nonlinear Schrödinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground‐state… read more here.
Keywords: quadratic interaction; system; schr dinger; nonlinear schr ... See more keywords
Ground states for a zero‐mass and Coulomb–Sobolev critical Schrödinger–Poisson–Slater problem
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DOI: 10.1002/mana.70058
Abstract: In this paper, we consider the following Schrödinger–Poisson–Slater equation: −Δu+14π|x|*|u|2u=μ|u|p−2u+|u|2u,inR3,$$\begin{equation*}\hspace*{35pt} -\Delta u+ \left(\frac{1}{4\pi |x|}\ast |u|^{2}\right)u=\mu |u|^{p-2}u+|u|^{2}u,\ \ \mathrm{in} \ \mathbb {R}^{3}, \nonumber \end{equation*}$$where μ>0$\mu >0$ and 3 read more here.
Keywords: poisson slater; schr dinger; dinger poisson;
Localization of the discrete one‐dimensional quasi‐periodic Schrödinger operators
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DOI: 10.1002/mma.10131
Abstract: In this paper, we study the spectral properties of a family of discrete one‐dimensional quasi‐periodic Schrödinger operators (depending on a phase theta). In large disorder, under some suitable conditions on v$$ v $$ and a… read more here.
Keywords: quasi periodic; schr dinger; dimensional quasi; one dimensional ... See more keywords
Ground state solutions for asymptotically linear Schrödinger equations on locally finite graphs
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DOI: 10.1002/mma.10145
Abstract: We are considered with the following nonlinear Schrödinger equation: −Δu+(λa(x)+1)u=f(u),x∈V,$$ -\Delta u+\left(\lambda a(x)+1\right)u=f(u),x\in V, $$ on a locally finite graph G=(V,E)$$ G=\left(V,E\right) $$ , where V$$ V $$ denotes the vertex set, E$$ E $$… read more here.
Keywords: schr dinger; asymptotically linear; state; ground state ... See more keywords
Traveling waves for a nonlinear Schrödinger system with quadratic interaction in ℝ4$$ {\mathrm{\mathbb{R}}}^4 $$
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DOI: 10.1002/mma.10158
Abstract: In this paper, we consider a nonlinear Schrödinger system with quadratic interaction. We extend the recent results of Fukaya et al. (Math. Ann. 2024) and show that the system has a ground state in ℝ4$$… read more here.
Keywords: system; system quadratic; schr dinger; quadratic interaction ... See more keywords
Instabilities of standing waves and positivity in traveling waves to a higher‐order Schrödinger equation
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DOI: 10.1002/mma.10315
Abstract: The aim of this paper is to explore a Schrödinger equation that incorporates a higher‐order operator. Traditional models for electron dynamics have utilized a second‐order diffusion Schrödinger equation, where oscillatory behavior is achieved through complex… read more here.
Keywords: equation; higher order; schr dinger; dinger equation ... See more keywords
Existence of stable standing waves for the critical fractional Schrödinger equation with an inhomogeneous combined nonlinearity
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DOI: 10.1002/mma.10335
Abstract: We study the orbitally stability of standing waves for the L2$$ {L}^2 $$ ‐critical inhomogeneous combined source term fractional nonlinear Schrödinger equation: i∂tu−(−Δ)su+a|x|−b|u|pu+|u|4sNu=0,(t,x)∈ℝ×ℝN$$ i{\partial}_tu-{\left(-\Delta \right)}^su+a{\left|x\right|}^{-b}{\left|u\right|}^pu+{\left|u\right|}^{\frac{4s}{N}}u=0,\left(t,x\right)\in \mathrm{\mathbb{R}}\times {\mathrm{\mathbb{R}}}^N $$ where N2N−1 read more here.
Keywords: x0005e; schr dinger; inhomogeneous combined; dinger equation ... See more keywords
Normalized solutions for Chern–Simons–Schrödinger system with mixed dispersion and critical exponential growth
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DOI: 10.1002/mma.10383
Abstract: This paper focuses on the existence of normalized solutions for the Chern–Simons–Schrödinger system with mixed dispersion and critical exponential growth. These solutions correspond to critical points of the underlying energy functional under the L2$$ {L}^2… read more here.
Keywords: system; schr dinger; solutions chern; chern simons ... See more keywords