Results 21 to 30 of about 21,370 (279)

Standing wave solutions of a quasilinear degenerate Schrödinger equation with unbounded potential

Electronic Journal of Qualitative Theory of Differential Equations, 2016
We are concerned with the existence of entire distributional nontrivial solutions for a new class of nonlinear partial differential equations. The differential operator was introduced by A. Azzolini et al.
Nejmeddine Chorfi, Vicenţiu Rădulescu
doaj   +1 more source

The intrinsic mountain pass principle [PDF]

Topological Methods in Nonlinear Analysis, 1998
The celebrated mountain pass principle of Ambrosetti and Rabinowitz is one of the most important tools in nonlinear analysis for proving the existence of critical points of \(C^1\) real functionals. The authors establish in this paper a general mountain pass principle, dropping any smoothness or even continuity assumptions on the functional.
Ribarska, Nadezhda, Tsachev, Tsvetomir, Krastanov, Mikhail   +2 more
openaire   +3 more sources

Conceptualising quality early childhood education: Learning from young children in Brazil and South Africa through creative and play‐based methods

British Educational Research Journal, EarlyView., 2023
Abstract Early childhood has increasingly been acknowledged as a vital time for all children. Inclusive and quality education is part of the United Nations Sustainable Development Goals, with the further specification that all children have access to quality pre‐primary education.
Laura H. V. Wright, Irene Rizzini, Malibongwe Gwele, Lynn McNair, Cristina Laclette Porto, Marsha Orgill, E. Kay M. Tisdall, Malcolm Bush, Linda Biersteker   +8 more
wiley   +1 more source

Nontrivial Solutions for Asymmetric Kirchhoff Type Problems

Abstract and Applied Analysis, 2014
We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞ in ℝN(N=2,3). Namely, it is 4-linear at −∞ and 4-superlinear at +∞.
Ruichang Pei, Jihui Zhang
doaj   +1 more source

Mountain Passes and Saddle Points

SIAM Review, 2015
Summary: Variational methods find solutions of equations by considering a solution as a critical point of an appropriately chosen function. Local minima and maxima are well-known types of critical points. We explore methods for finding critical points that are neither local maxima or minima, but instead are mountain passes or saddle points.
openaire   +3 more sources

GENERAL QUASILINEAR PROBLEMS INVOLVING \(p(x)\)-LAPLACIAN WITH ROBIN BOUNDARY CONDITION

Ural Mathematical Journal, 2020
This paper deals with the existence and multiplicity of solutions for a class of quasilinear problems involving \(p(x)\)-Laplace type equation, namely $$ \left\{\begin{array}{lll} -\mathrm{div}\, (a(| \nabla u|^{p(x)})| \nabla u|^{p(x)-2} \nabla u ...
Hassan Belaouidel, Anass Ourraoui, Najib Tsouli   +2 more
doaj   +1 more source

Copper‐based Materials for Photo and Electrocatalytic Process: Advancing Renewable Energy and Environmental Applications

Advanced Functional Materials, EarlyView.
Cu‐based catalysts as a cornerstone in advancing sustainable energy technologies are fully reviewed in this manuscript, highlighting their potential in photo‐ and electrocatalysis. It includes metallic copper, copper oxides, copper sulfides, copper halide perovskites, copper‐based metal–organic frameworks (MOFs), and covalent organic frameworks (COFs),
Jéssica C. de Almeida, Yanjie Wang, Thais A. Rodrigues, Paulo H. H. Nunes, Vagner R. de Mendonça, Paulo H. E. Falsetti, Leticia V. Savazi, Tao He, Alexandra V. Bardakova, Aida V. Rudakova, Jie Tian, Alexei V. Emeline, Osmando F. Lopes, Antonio Otavio T. Patrocínio, Jia Hong Pan, Caue Ribeiro, Detlef W. Bahnemann   +16 more
wiley   +1 more source

ГОРНЫЙ УДАР – ПРИЧИНА ВЫБРОСА МЕТАНА В УГОЛЬНОЙ ШАХТЕ?

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2015
Предложена модель, в которой горный удар (техногенное землетрясение) – представлен как выход ударной волны на внутреннюю стенку шахты. При этом возникает волна разгрузки, растяжения, двигающаяся в обратном (вглубь стенки) направлении.
В.В.Кузнецов, V.V. Kuznetsov
doaj   +1 more source

Microbubble Shell Stiffness Engineering Enhances Ultrasound Imaging, Drug Delivery, and Sonoporation

Advanced Materials, EarlyView.
 Shell‐engineered poly(alkyl cyanoacrylate) microbubbles with tunable stiffness improve ultrasound imaging and therapy. Adjusting the length of the alkyl chain and the glass transition temperature maintains a narrow microbubble size distribution while enhancing drug loading, sonoporation and the acoustic response.
Roman A. Barmin, MirJavad Moosavifar, Elena Rama, Julia Blöck, Anne Rix, Vladislav S. Petrovskii, Rustam A. Gumerov, Jens Köhler, Michael Pohl, Céline Bastard, Stephan Rütten, Laura Charlton, Vu Ngoc Khiêm, Fabio Domenici, Thomas Lisson, Ekaterina Savina, Rui Zhang, Jasmin Baier, Susanne Koletnik, Vasileios Koutsos, Mikhail Itskov, Gaio Paradossi, Georg Schmitz, Tina Vermonden, Laura De Laporte, Robert Göstl, Andreas Herrmann, Igor I Potemkin, Fabian Kiessling, Twan Lammers, Roger M. Pallares   +30 more
wiley   +1 more source

The existence and multiplicity of L 2-normalized solutions to nonlinear Schrödinger equations with variable coefficients

Advanced Nonlinear Studies
The existence of L 2–normalized solutions is studied for the equation −Δu+μu=f(x,u)  inRN,∫RNu2dx=m. $-{\Delta}u+\mu u=f\left(x,u\right)\quad \quad \text{in} {\mathbf{R}}^{N},\quad {\int }_{{\mathbf{R}}^{N}}{u}^{2} \mathrm{d}x=m.$ Here m > 0 and f(x, s)
Ikoma Norihisa, Yamanobe Mizuki
doaj   +1 more source