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$$ {L}^2… read more here.
Keywords: system; schr dinger; solutions chern; chern simons ... See more keywords
Normalized Sign‐Changing Solutions for the Nonlinear Schrödinger Equation With a Mass‐Critical Perturbation
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DOI: 10.1002/mma.10954
Abstract: We investigate the mass‐critical perturbed nonlinear Schrödinger equation with a prescribed mass and establish the existence of sign‐changing normalized solutions in noncompact settings for N≥4$$ N\ge 4 $$ . Additionally, we analyze the asymptotic behavior… read more here.
Keywords: schr dinger; sign changing; normalized solutions; dinger equation ... See more keywords
Existence of Normalized Solutions of a Hartree–Fock System With Mass Subcritical Growth
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DOI: 10.1002/mma.11028
Abstract: In this paper, we are concerned with normalized solutions of a class of Hartree‐Fock type systems. By seeking the constrained global minimizers of the corresponding functional, we prove that the existence and nonexistence of normalized… read more here.
Keywords: solutions hartree; fock system; existence normalized; hartree fock ... See more keywords
Normalized Solutions to Quasilinear Choquard Equations With a Local Perturbation
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DOI: 10.1002/mma.11212
Abstract: In this paper, we study the Choquard equation involving the p$$ p $$ ‐Laplacian operator with a Lp$$ {L}^p $$ ‐norm constraint. We present Gagliardo‐Nirenberg inequality of Hartree type with best constant in the p$$… read more here.
Keywords: equations local; solutions quasilinear; perturbation; choquard equations ... See more keywords
Normalized Solutions to a Quasilinear Equation Involving Critical Sobolev Exponent
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DOI: 10.1002/mma.70212
Abstract: In this paper, we study the normalized solutions of a quasilinear elliptic Choquard equation with critical Sobolev exponent and a mixed diffusion‐type operator. The study begins by demonstrating the Hölder regularity of a weak solution,… read more here.
Keywords: equation; sobolev exponent; solutions quasilinear; critical sobolev ... See more keywords
Normalized solutions to the Chern–Simons–Schrödinger system: the supercritical case
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DOI: 10.1007/s11784-025-01186-3
Abstract: We are concerned with the existence of normalized solutions for a class of generalized Chern–Simons–Schrödinger type problems with supercritical exponential growth -Δu+λu+A0u+∑j=12Aj2u=f(u),∂1A2-∂2A1=-12|u|2,∂1A1+∂2A2=0,∂1A0=A2|u|2,∂2A0=-A1|u|2,∫R2|u|2dx=a2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\{ \begin{array}{ll} \displaystyle -\Delta… read more here.
Keywords: end; document; usepackage; chern simons ... See more keywords
Normalized solutions for a coupled Schrödinger system with saturable nonlinearities
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DOI: 10.1016/j.jmaa.2017.10.057
Abstract: Abstract We study the existence of prescribed L 2 -norm solutions for the coupled Schrodinger system with saturable nonlinearities, which appears in models for propagation of a beam with two mutually incoherent components in a… read more here.
Keywords: system saturable; normalized solutions; solutions coupled; saturable nonlinearities ... See more keywords
Normalized solutions for an horizontal transmission problem
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DOI: 10.1080/00036811.2020.1712371
Abstract: ABSTRACT Let Ω be a bounded and smooth domain in . We study in this paper the following nonlinear transmission problem where the unknowns are and the real numbers . Actually we are looking for… read more here.
Keywords: horizontal transmission; normalized solutions; transmission problem; problem ... See more keywords
Multiple positive normalized solutions for nonlinear Schrödinger systems
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DOI: 10.1088/1361-6544/aab0bf
Abstract: We consider the existence of multiple positive solutions to the nonlinear Schrodinger systems set on , under the constraint Here are prescribed, , and the frequencies are unknown and will appear as Lagrange multipliers. Two… read more here.
Keywords: solutions nonlinear; nonlinear schr; normalized solutions; multiple positive ... See more keywords
Normalized solutions for the fractional Schrödinger equation with combined nonlinearities
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DOI: 10.1515/forum-2023-0424
Abstract: Abstract In this paper, we study the normalized solutions for the following fractional Schrödinger equation with combined nonlinearities { ( - Δ ) s u = λ u + μ | u… read more here.
Keywords: schr dinger; combined nonlinearities; normalized solutions; dinger equation ... See more keywords
Normalized solutions for nonlinear Schrödinger-Poisson equations involving nearly mass-critical exponents
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DOI: 10.3934/cpaa.2025077
Abstract: We study the Schr\"{o}dinger-Poisson-Slater equation \begin{equation*}\left\{\begin{array}{lll} -\Delta u + \lambda u + \big(|x|^{-1} \ast |u|^{2}\big)u = V(x) u^{ p_{\varepsilon}-1 }, \, \text{ in } \mathbb{R}^{3},\\[2mm] \int_{\mathbb{R}^3}u^2 \,dx= a,\,\, u>0,\,\, u \in H^{1}(\mathbb{R}^{3}), \end{array} \right. \end{equation*}… read more here.
Keywords: schr dinger; solutions nonlinear; varepsilon; dinger poisson ... See more keywords