Results 91 to 100 of about 428,921 (359)
Singular nonlinear elliptic equations in Rn
Abstract and Applied Analysis, 1998 This paper deals with existence, uniqueness and regularity of positive generalized solutions of singular nonlinear equations of the form −Δu+a(x)u=h(x)u−γ in Rn where a,h are given, not necessarily continuous functions, and γ is a positive number.
C. O. Alves, J. V. Goncalves, L. A. Maia
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Nonlinear Stability for Dissipative Nonlinear Evolution Equations with Ellipticity
Journal of Mathematical Analysis and Applications, 1999 The paper deals with the coupled system \[ \psi_t=-(1-\alpha)\psi-\sigma \theta_x +\alpha\psi_{xx}, \] \[ \theta_t=-(1-\alpha)\theta+\nu \psi_x +2\psi \theta_{x}+\alpha\theta_{xx}, \] where \(\alpha\) and \(\nu\) are positive numbers. This set of equations singles out the essential mechanism of nonlinear interaction between ellipticity and dissipation.
Tang, Shaoqiang, Zhao, Huijiang
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Optically Driven Formation of Tailored Phonon Cavities
Advanced Science, EarlyView.It is demonstrated that a structured optical field creates nanoscale “phonon cavities” in van der Waals materials, where atomic vibrations are confined and controlled in space and time. This approach enables programmable control of cavity geometry, symmetry, and frequency, and provides a platform for ultrafast studies of nonequilibrium interactions and
Jianyu Wu +5 more
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Bounds and compactness for solutions of second-order elliptic equations
Electronic Journal of Differential Equations, 2012 In this article, we establish some connections between Sobolev spaces and nonlinear singular elliptic problems, to obtain bounds and compactness results for solutions of second-order elliptic equations.
Carlos C. Aranda
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Calculus of Variations and Partial Differential Equations, 2019 In this paper, we study a nonlinear Dirichlet problem of p-Laplacian type with combined effects of nonlinear singular and convection terms. An existence theorem for positive solutions is established as well as the compactness of solution set.
Zhenhai Liu, D. Motreanu, Shengda Zeng
semanticscholar +1 more source
Advanced Science, EarlyView.By exploiting the strong nonlinear optical response and controllable molecular ordering of ferroelectric nematic liquid crystals (FNLCs), these materials can serve as tunable sources of polarization‐entangled photons. Adjusting the sample geometry or applying an external electric field enables continuous control of the entanglement degree, advancing ...
Sara Klopčič +3 more
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A stability result for elliptic equations with singular nonlinearity and its applications to homogenization problems [PDF]
, 2021 Takanobu Hara
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Nanoscopic Mapping of the Extracellular Space in Amyloid Plaque‐rich Cortex
Advanced Science, EarlyView.The extracellular space and diffusion around amyloid plaques are examined using shadow imaging and single‐particle tracking. Increased diffusivity is found near plaques, extracellular matrix alterations, and plaque core penetrability that varies with amyloid phenotype.
Juan Estaún‐Panzano +11 more
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Lower-order perturbations of critical growth nonlinearities in semilinear elliptic equations [PDF]
, 1997 Filippo Gazzola, Bernhard Ruf
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Helix Alignment, Chevrons, and Edge Dislocations in Twist‐Bend Ferroelectric Nematics
Advanced Science, EarlyView.The recently discovered twist‐bend ferroelectric nematic (NTBF) is the new member of the multiferroic family, representing a fluid with an oblique helicoidal (heliconical) periodic structure of spontaneous electric polarization. The work presents a thorough exploration of the material properties of this phase, how the periodic modulation of ...
Bijaya Basnet +8 more
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