Existence and uniqueness of damped solutions of singular IVPs with phi-Laplacian

We study analytical properties of a singular nonlinear ordinary differential equation with a phi-Laplacian. In particular we investigate solutions of the initial value problem (p(t)phi(u'(t)))' + p(t)f(phi(u(t))) = 0, u(0) = u(0) is an element of [L-0, L], u'(0) = 0 on the half-line [0, infinity). Here, f is a continuous function with three zeros phi(L0) < 0 < phi(L), function p is positive on (0, infinity) and the problem is singular in the sense that p(0) - 0 and 1/p(t) may not be integrable on [0,1]. The main goal of the paper is to prove the existence of damped solutions defined as solutions u satisfying sup{u(t), t is an element of [0, infinity)} < L. Moreover, we study the uniqueness of damped solutions. Since the standard approach based on the Lipschitz property is not applicable here in general, the problem is more challenging. We also discuss the uniqueness of other types of solutions.Web of Science12128

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Nonlinear Differential Equations on Bounded and Unbounded Domains

Differential equations represent one of the strongest connections between Mathematics and real life. This is due to the fact that almost all the physical phenomena, as well as many other in economy, biology or chemistry, are modelled by differential equations. This Thesis includes a detailed study of nonlinear differential equations, both on bounded and unbounded domains. In particular, we analyze the qualitative properties of the solutions of nonlinear differential equations, focusing on the study of constant sign solutions on the whole domain of definition or, at least, on some subset of it. The main technique is based on the construction of an abstract formulation included into functional analysis, in which the solutions of the differential equations coincide with the fixed points of certain operators

Sonic and Vibration Environments for Ground Facilities: a Design Manual

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