Results 101 to 110 of about 12,072 (286)

Infinitely many solutions for a class of Kirchhoff-type equations

Open Mathematics
In this article, we consider a class of Kirchhoff-type equations: −a+b∫Ω∣∇u∣2dxΔu=f(x,u),x∈Ω,u=0,x∈∂Ω.\left\{\begin{array}{ll}-\left(a+b\mathop{\displaystyle \int }\limits_{\Omega }{| \nabla u| }^{2}{\rm{d}}x\right)\Delta u=f\left(x,u),\hspace{1.0em}& x ...
Zhou Qin, Zeng Jing
doaj   +1 more source

Negotiating in a Foreign Land: Understanding the Curious Interactions Between Intracellular Mitochondria and Internalized Nanoparticles

Advanced Materials Interfaces, EarlyView.
Therapeutic nano‐drug delivery systems interact with cellular mitochondria in a multitude of ways. While the complexity of such interactions disrupts the mitochondrial electron transport chain and increases reactive oxygen species production, thereby contributing to nanoparticle toxicity, they also present unique theranostic opportunities in diseases ...
Sourav Bhattacharjee
wiley   +1 more source

Infinitely many solutions for Hamiltonian system with critical growth

Advances in Nonlinear Analysis
In this article, we consider the following elliptic system of Hamiltonian-type on a bounded domain:−Δu=K1(∣y∣)∣v∣p−1v,inB1(0),−Δv=K2(∣y∣)∣u∣q−1u,inB1(0),u=v=0on∂B1(0),\left\{\begin{array}{ll}-\Delta u={K}_{1}\left(| y| ){| v| }^{p-1}v,\hspace{1.0em ...
Guo Yuxia, Hu Yichen
doaj   +1 more source

Deterministic Integration of Quantum Emitters and Optical Cavities in a Van Der Waals Crystal

Advanced Optical Materials, EarlyView.
The work demonstrates fabrication of Circular Bragg Grating (CBG) cavities with embedded emitters in hBN. The cavities are fabricated around a pre‐characterised quantum emitter. The integrated platform enables light matter interaction and access to brighter emitters and spins in hBN.
James Liddle‐Wesolowski, Otto Cranwell Schaeper, Nathan Coste, Benjamin Whitefield, Evan Williams, Helen Zhi Jie Zeng, Mehran Kianinia, Anastasiia Zalogina, Igor Aharonovich   +8 more
wiley   +1 more source

Infinitely many weak solutions for a mixed boundary value system with $(p_1,...p_m)$-Laplacian

Electronic Journal of Qualitative Theory of Differential Equations, 2014
The aim of this paper is to prove the existence of infinitely many weak solutions for a mixed boundary value system with $(p_1,\dots,p_m)$-Laplacian. The approach is based on variational methods.
Diego Averna, Elisabetta Tornatore
doaj   +1 more source

Infinitely many radial solutions of an elliptic system [PDF]

Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 1987
We consider a system of equations of the form Δu + ∇F(u) = 0 . In this and two subsequent papers we find conditions on F(u) to guarantee that this system has infinitely many radial solutions.
openaire   +2 more sources

AI‐Powered Framework for Evaluating Drug Efficacy for Three‐Dimensional In Vitro Cancer Models in Robot‐Assisted Production

Advanced Robotics Research, EarlyView.
An AI‐powered, robot‐assisted framework automatically produces, images, and analyzes 3D tumor spheroids to evaluate drug efficacy. Integrated modules handle spheroid formation, live/dead staining, brightfield imaging, and automated image analysis, including spheroid segmentation, viability and metrics to assess the drug treatment efficacy. The workflow
Dalia Mahdy, Jesus Nieves, Lukas Königer, Matthias Peindl, Fabio Erhard, Marc Möllmann, Anke Klingner, Markus Münig, Bibin Babu, Thomas Schwarz, Marco Metzger, Gudrun Dandekar, Maximiliane Wußmann, Jan Hansmann   +13 more
wiley   +1 more source

Infinitely many solutions for polyharmonic elliptic problems with broken symmetries [PDF]

, 2003
By means of a perturbation argument devised by P. Bolle, we prove the existence of infinitely many solutions for perturbed symmetric polyharmonic problems with non­homogeneous Dirichlet boundary conditions.
Lancelotti, Sergio, S. Lancelotti, Squassina, M., Musesti, A., Squassina, Marco, SQUASSINA M., Marco Squassina, A. Musesti, MUSESTI A., Alessandro Musesti, Musesti, Alessandro, Sergio Lancelotti   +11 more
core   +1 more source

Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations

Abstract and Applied Analysis, 2013
Several new existence theorems on positive, negative, and sign-changing solutions for the following fourth-order beam equation are obtained: u(4)=f(t,u(t)),   t∈[0,1];  u(0)=u(1)=u′′(0)=u′′(1)=0, where f∈C([0,1]×ℝ1,ℝ1).
Ying Wu, Guodong Han
doaj   +1 more source

Infinitely many solutions for Kirchhoff type problems [PDF]

Differential Equations & Applications, 2013
This paper is devoted to the study of infinitely many solutions for a class of Kirchhoff type problems on a bounded domain. Based on the Fountain Theorem of Bartsch, we obtain the multiplicity results, which unify and sharply improve the recent results of He and Zou [X. He, W.
openaire   +1 more source