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Global multiplicity of solutions to a defocusing quasilinear Schrodinger equation with the singular term

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Science China Mathematics 2023年第8期66卷 1789-1812页

作者： Siyu Chen Carlos Alberto Santos Minbo Yang Jiazheng Zhou department of Mathematics Zhejiang Normal UniversityJinhua 321004China departamento de matematica Universidade de BrasiliaBraslia 70910-900Brazil

We consider a class of modified quasilinear Schrodinger equations-△u+k/2u△u^(2)=λα(x)u^(-α)+b(x)u^(β) in Ω with u(x)=0 on■Ω,where Ω■R^(N)is a bounded domain with a regular boundary,N≥3,a and b are bounded mensurable functions,0<α<1<β<2*-1 and k,λ≥0 are two parameters.We establish the global existence and multiplicity results of positive solutions in H^(1)_(0)(Ω)∩L^(∞)(Ω)for appropriate classes of parameters k andλand coefficients a(x)and b(x).

关键词： quasilinear Schrodinger equation singular term square diffusion term

Free Cyclic Actions on Surfaces and the Borsuk-Ulam Theorem

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Acta Mathematica Sinica,English Series 2022年第10期38卷 1803-1822页

作者： Daciberg Lima GONCALVES John GUASCHI Vinicius Casteluber LAASS departamento de matematica IMEUniversidade de Sao PauloRua do Matao 1010 CEP:05508-090Sao Paulo-SPBrazil Normandie Univ. UNICAENCNRSLMNO14000 CaenFrance Universidade Federal da Bahia IMEDepartamento de MatematicaAv.Milton SantosS/N Ondina CEP:40170-110Salvador-BABrazil

Let M and N be topological spaces,let G be a group,and letτ:G×M→M be a proper free action of G.In this paper,we define a Borsuk-Ulam-type property for homotopy classes of maps from M to N with respect to the pair(G,τ)that generalises the classical antipodal Borsuk-Ulam theorem of maps from the n-sphere S^(n) to R^(n).In the cases where M is a finite pathwise-connected CWcomplex,G is a finite,non-trivial Abelian group,τis a proper free cellular action,and N is either R^(2) or a compact surface without boundary different from S^(2) and RP^(2),we give an algebraic criterion involving braid groups to decide whether a free homotopy class β∈[M,N]has the Borsuk-Ulam property.As an application of this criterion,we consider the case where M is a compact surface without boundary equipped with a free actionτof the finite cyclic group Zn.In terms of the orient ability of the orbit space Mof M by the actionτ,the value of n modulo 4 and a certain algebraic condition involving the first homology group of M,we are able to determine if the single homotopy class of maps from M to R^(2) possesses the Borsuk-Ulam property with respect to(Z_(n),τ).Finally,we give some examples of surfaces on which the symmetric group acts,and for these cases,we obtain some partial results regarding the Borsuk-Ulam property for maps whose target is R^(2).

关键词： Borsuk-Ulam theorem cyclic groups braid groups surfaces

PHASE PORTRAITS OF THE LESLIE-GOWER SYSTEM

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Acta Mathematica Scientia 2022年第5期42卷 1734-1742页

作者： Jaume LLIBRE Claudia VALLS departament de Matematiques Universitat Autonoma de Barcelona08193BellaterraBarcelonaCataloniaSpain departamento de matematica Instituto Superior TecnicoUniversidade de LisboaAu.Rovisco Pais 1049-001LisboaPortugal

In this paper we characterize the phase portraits of the Leslie-Gower model for competition among species.We give the complete description of their phase portraits in the Poincarédisc(i.e.,in the compactification of R^(2) adding the circle S1 of the infinity)modulo topological equivalence.It is well-known that the equilibrium point of the Leslie-Gower model in the interior of the positive quadrant is a global attractor in this open quadrant,and in this paper we characterize where the orbits attracted by this equilibrium born.

关键词： predator-prey models Leslie-Gower system Poincare compactification global phaseportraits

NUMERICAL ANALYSIS OF A PROBLEM INVOLVING A VISCOELASTIC BODY WITH DOUBLE POROSITY

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Journal of Computational Mathematics 2022年第3期40卷 415-436页

作者： Noelia Bazarra Jose R.Fernandez MariCarme Leseduarte Antonio Magana Ramon Quintanilla departamento de matematica Aplicada I Universidade de VigoETSI TelecomunicacionCampus As Lagoas Marcosende s/n36310 VigoSpain departamento de matematicas E.S.E.I.A.A.T.-U.P.C.Colom 1108222 TerrassaBarcelonaSpain

We study from a numerical point of view a multidimensional problem involving a viscoelastic body with two porous structures.The mechanical problem leads to a linear system of three coupled hyperbolic partial differential equations.Its corresponding variational formulation gives rise to three coupled parabolic linear equations.An existence and uniqueness result,and an energy decay property,are recalled.Then,fully discrete approximations are introduced using the finite element method and the implicit Euler scheme.A discrete stability property and a priori error estimates are proved,from which the linear convergence of the algorithm is derived under suitable additional regularity conditions.Finally,some numerical simulations are performed in one and two dimensions to show the accuracy of the approximation and the behaviour of the solution.

关键词： Viscoelasticity with double porosity Finite elements A priori estimates Numerical simulations

Existence and Multiplicity Results for a Class of Nonlinear Schrödinger Equations with Magnetic Potential Involving Sign-Changing Nonlinearity

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Analysis in Theory and Applications 2022年第2期38卷 148-177页

作者： Francisco Odair de Paiva Sandra Machado de Souza Lima Olimpio Hiroshi Miyagaki departamento de matematica UFSCarSao CarlosSP13560-970 Brazil departamento de Ciencias Exatas Biologicas e da TerraINFES-UFFSanto Antonio de Padua-RJ28470-000Brazil

In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2 详细信息

In this work we consider the following class of elliptic problems{−Δ_(A)u+u=a(x)|u|^(q−2)u+b(x)|u|^(p−2)u in R^(N),u∈H_(A)^(1)(R^(N)),(P)with 2

关键词： Magnetic potential sign-changing weight functions Nehari manifold Fibering map

COMPLEXITY OF LARGE TIME BEHAVIOUR OF EVOLUTION EQUATIONS WITH BOUNdeD DATA

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Chinese Annals of Mathematics,Series B 2002年第2期23卷 293-310页

作者： J.L.VZQUEZ E.ZUAZUA departamento de matematicas Universidad AutonomaDepartamento de Matematica AplicadaUniversidadComplutense 28049MadridSpain28040 M

The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.

关键词：复杂性大时间行为发展方程有界数据热方程 Omega极限双曲守恒定律半群收敛性

Simple Classical Lie Algebras in Characteristic 2 and Their Gradations, II

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Algebra Colloquium 2014年第2期21卷 207-214页

作者： Alexandre N. Grishkov Marines Guerreiro Instituto de matematica e Estatfstica Universidade de Sao Paulo Sao Paulo-SP Brazil departamento de matematica Universidade Federal de Vicosa Vicosa-MG Brazil

This paper is a continuation of [2]. We prove Conjecture 5.1 of [2] which gives a characterization of simple Lie algebras of finite dimension of type B2e, C2e, D2e＋1, E7 and Es in terms of some gradations of these al... 详细信息

关键词： Lie algebras characteristic 2 gradations

A Weierstrass Representation Formula for Minimal Surfaces in H_3 and H^2×R

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1603-1612页

作者： Francesco MERCURI StefanoMONTALDO PaolaPIU departamento de matematica.C.P.6065 IMECCUNICAMP UniversitàdegliStudi di Cagliari Dipartimento di Matematica

We give a general setting for constructing a Weierstrass representation formula for simply connected minimal surfaces in a Riemannian manifold. Then, we construct examples of minimal surfaces in the three dimensional ... 详细信息

关键词： Minimal immersions Weierstrass representation Heisenberg group Hyperbolic space

On the Spectra of a Family of Geometric Operators Evolving with Geometric Flows

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Communications in Mathematics and Statistics 2021年第2期9卷 181-202页

作者： D.M.Tsonev R.R.Mesquita departamento de matematica UFAMManausAM 69077-070Brazil

In this work we generalise various recent results on the evolution and monotonicity of the eigenvalues of certain family of geometric operators under some geometric flows.In an attempt to understand the arising similarities we formulate two conjectures on the monotonicity of the eigenvalues of Schrodinger operators under geometric flows.We also pose three questions which we consider to be of a general interest.

关键词： Witten-Laplacian Eigenvalues Monotonicity of eigenvalues Ricci flow Ricci–Bourguignon flow Yamabe flow Bochner formula Reilly formula