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Topological and Variational Methods for Differential Equations
These notes contain the extended abstracts of the talks presented at the workshop. The range of topics includes nonlinear SchroÌdinger equations, singularly perturbed equations, symmetry and nodal properties of solutions, long-time dynamics for parabolic equations, Morse theory
Stability Analysis of Plates and Shells
This special publication contains the papers presented at the special sessions honoring Dr. Manuel Stein during the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference held in Kissimmee, Florida, Apdl 7-10, 1997. This volume, and the SDM special sessions, are dedicated to the memory of Dr. Manuel Stein, a major pioneer in structural mechanics, plate and shell buckling, and composite structures. Many of the papers presented are the work of Manny's colleagues and co-workers and are a result, directly or indirectly, of his influence. Dr. Stein earned his Ph.D. in Engineering Mechanics from Virginia Polytechnic Institute and State University in 1958. He worked in the Structural Mechanics Branch at the NASA Langley Research Center from 1943 until 1989. Following his retirement, Dr. Stein continued his involvement with NASA as a Distinguished Research Associate
Resultados de multiplicidade para sistemas do tipo Schrödinger-Poisson
Doutoramento conjunto em Matemåtica - Matemåtica e AplicaçÔes (PDMA)In this thesis, we study the existence and multiplicity of solutions of the
following class of Schr odinger-Poisson systems:
u + u + l(x) u = (x; u) in R3;
= l(x)u2 in R3;
where l 2 L2(R3) or l 2 L1(R3). And we consider that the nonlinearity
satis es the following three kinds of cases:
(i) a subcritical exponent with (x; u) = k(x)jujp2u + h(x)u (4 p <
2 ) under an inde nite case;
(ii) a general inde nite nonlinearity with (x; u) = k(x)g(u) + h(x)u;
(iii) a critical growth exponent with (x; u) = k(x)juj2 2u +
h(x)jujq2u (2 q < 2 ).
It is worth mentioning that the thesis contains three main innovations except
overcoming several di culties, which are generated by the systems themselves.
First, as an unknown referee said in his report, we are the rst authors
concerning the existence of multiple positive solutions for Schr odinger-
Poisson systems with an inde nite nonlinearity.
Second, we nd an interesting phenomenon in Chapter 2 and Chapter 3
that we do not need the condition
R
R3 k(x)ep
1dx < 0 with an inde nite noncoercive
case, where e1 is the rst eigenfunction of +id in H1(R3) with
weight function h. A similar condition has been shown to be a su cient
and necessary condition to the existence of positive solutions for semilinear
elliptic equations with inde nite nonlinearity for a bounded domain (see
e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475), or to be
a su cient condition to the existence of positive solutions for semilinear
elliptic equations with inde nite nonlinearity in RN (see e.g. Costa-Tehrani,
Calc. Var. PDE 13 (2001), 159{189). Moreover, the process used in
this case can be applied to study other aspects of the Schr odinger-Poisson
systems and it gives a way to study the Kirchho system and quasilinear
Schr odinger system.
Finally, to get sign changing solutions in Chapter 5, we follow the spirit of
Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137 (2007), 333, but
the procedure is simpler than that they have proposed in their paper.Nesta tese, estudamos a existĂȘncia e a multiplicidade de soluçÔes da seguinte
classe de sistemas denominada de Schr odinger-Poisson:
u + u + l(x) u = (x; u) in R3;
= l(x)u2 in R3; onde l 2 L2(R3) ou l 2 L1(R3). Consideram-se nĂŁo-linearidades que
satisfazem um dos seguintes casos:
(i) potĂȘncias que envolvem um expoente sub-cr tico, da forma (x; u) =
k(x)jujp2u + h(x)u, (4 p < 2 ), sendo k uma função com sinal
indefinido e h uma função positiva;
(ii) caso geral de uma nĂŁo-linearidade indefi nida, da forma (x; u) =
k(x)g(u) + h(x)u, sendo k uma função com sinal indefinido e h uma função positiva;
(iii) potĂȘncias que envolvem o expoente crĂ tico, da forma (x; u) =
k(x)juj2 2u + h(x)jujq2u (2 q < 2 ).
ConvĂ©m salientar que esta tese tem trĂȘs principais inovaçÔes, as quais
ultrapassam dificuldades geradas pela natureza dos problemas estudados.
Primeiro, como um relator anĂłnimo referiu, este Ă© o primeiro trabalho em
que se trata a existĂȘncia de vĂĄrias soluçÔes de sistemas de Schrödinger-
Poisson com nĂŁo-linearidade indefinida.
Segundo, neste estudo encontrou-se um fen Ăłmeno interessante, ver
CapĂtulos 2 e 3, nomeadamente, nĂŁo ser necess ĂĄria a condição R3 k(x)ep
1dx < 0 no caso indefinido e não-coercivo, sendo e1 a função
associada ao primeiro valor prĂłprio de + id em H1(R3) com peso
h. Note-se que foi demonstrado que uma condi cão semelhante e condição
necessĂĄria e suficiente na existĂȘncia de solu cĂ”es positivas para equaçÔes
elĂticas semilineares com nĂŁo-linearidades indefinidas em domĂnios limitados
(ver e.g. Alama-Tarantello, Calc. Var. PDE 1 (1993), 439{475),
ou ser uma condição suficiente na existĂȘncia de soluçÔes positivas para
equaçÔes elĂticas semilineares com nĂŁo-linearidades indefinidas em RN (see
e.g. Costa-Tehrani, Calc. Var. PDE 13 (2001), 159{189). Adicionalmente, o método utilizado pode ser utilizado para estudar outros aspetos dos sistemas de Schrodinger-Poisson, permite também estudar sistemas de
Kirchho e sistemas de Schrodinger quasilineares.
Por m, para obter soluçÔes com mudança de sinal no Cap. 5, segue se
a ideia de Hirano-Shioji, Proc. Roy. Soc. Edinburgh Sect. A 137
(2007), 333, mas o método utilizado é uma versão simplificada do método
apresentado no artigo referido
Mathematical foundations of elasticity
[Preface] This book treats parts of the mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It is intended for mathematicians, engineers, and physicists who wish to see this classical subject in a modern setting and to see some examples of what newer mathematical tools have to contribute
Research in structural and solid mechanics, 1982
Advances in structural and solid mechanics, including solution procedures and the physical investigation of structural responses are discussed
Mathematical and Numerical Aspects of Dynamical System Analysis
From Preface: This is the fourteenth time when the conference âDynamical Systems: Theory and Applicationsâ gathers a numerous group of outstanding scientists and engineers, who deal with widely understood problems of theoretical and applied dynamics. Organization of the conference would not have been possible without a great effort of the staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over the conference has been taken by the Committee of Mechanics of the Polish Academy of Sciences and Ministry of Science and Higher Education of Poland. It is a great pleasure that our invitation has been accepted by recording in the history of our conference number of people, including good colleagues and friends as well as a large group of researchers and scientists, who decided to participate in the conference for the first time. With proud and satisfaction we welcomed over 180 persons from 31 countries all over the world. They decided to share the results of their research and many years experiences in a discipline of dynamical systems by submitting many very interesting papers. This year, the DSTA Conference Proceedings were split into three volumes entitled âDynamical Systemsâ with respective subtitles: Vibration, Control and Stability of Dynamical Systems; Mathematical and Numerical Aspects of Dynamical System Analysis and Engineering Dynamics and Life Sciences. Additionally, there will be also published two volumes of Springer Proceedings in Mathematics and Statistics entitled âDynamical Systems in Theoretical Perspectiveâ and âDynamical Systems in Applicationsâ
14th Conference on Dynamical Systems Theory and Applications DSTA 2017 ABSTRACTS
From Preface:
This is the fourteen time when the conference âDynamical Systems â Theory and
Applicationsâ gathers a numerous group of outstanding scientists and engineers, who deal with
widely understood problems of theoretical and applied dynamics.
Organization of the conference would not have been possible without a great effort of the
staff of the Department of Automation, Biomechanics and Mechatronics. The patronage over
the conference has been taken by the Committee of Mechanics of the Polish Academy of
Sciences and the Ministry of Science and Higher Education.
It is a great pleasure that our invitation has been accepted by so many people, including good
colleagues and friends as well as a large group of researchers and scientists, who decided to
participate in the conference for the first time. With proud and satisfaction we welcome nearly
250 persons from 38 countries all over the world. They decided to share the results of their
research and many years experiences in the discipline of dynamical systems by submitting many
very interesting papers.
This booklet contains a collection of 375 abstracts, which have gained the acceptance of
referees and have been qualified for publication in the conference proceedings [...]