The aim of this book is to provide a concise but complete introduction to the main mathematical tools of nonlinear functional analysis, which are also used in the study of concrete problems in ...economics, engineering, and physics. This volume gathers the mathematical background needed in order to conduct research or to deal with theoretical problems and applications using the tools of nonlinear functional analysis. Contents Basic Topology Measure Theory Basic Functional Analysis Banach Spaces of Functions and Measures Convex Functions - Nonsmooth Analysis Nonlinear Analysis
The vascular endothelium is a monolayer of cells between the vessel lumen and the vascular smooth muscle cells. Nitric oxide (NO) is a soluble gas continuously synthesized from the amino acid ...L-arginine in endothelial cells by the constitutive calcium-calmodulin-dependent enzyme nitric oxide synthase (NOS). This substance has a wide range of biological properties that maintain vascular homeostasis, including modulation of vascular dilator tone, regulation of local cell growth, and protection of the vessel from injurious consequences of platelets and cells circulating in blood, playing in this way a crucial role in the normal endothelial function. A growing list of conditions, including those commonly associated as risk factors for atherosclerosis such as hypertension, hypercholesterolemia, smoking, diabetes mellitus and heart failure are associated with diminished release of nitric oxide into the arterial wall either because of impaired synthesis or excessive oxidative degradation. The decreased production of NO in these pathological states causes serious problems in endothelial equilibrium and that is the reason why numerous therapies have been investigated to assess the possibility of reversing endothelial dysfunction by enhancing the release of nitric oxide from the endothelium. In the present review we will discuss the important role of nitric oxide in physiological endothelium and we will pinpoint the significance of this molecule in pathological states altering the endothelial function.
Abstract
In this paper, we consider an abstract system which consists of a nonlinear differential inclusion and a parabolic hemivariational inequality (DPHVI) in Banach spaces. The objective of this ...paper is four fold. The first target is to deal with the existence of solutions and the properties which involve the boundedness and continuous dependence results of the solution set to parabolic hemivariational inequality. The second aim is to investigate the existence of mild solutions to DPHVI by means of a fixed point technique. The third one is to study the existence of a pullback attractor for the multivalued processes governed by DPHVI. Finally, the fourth goal is to demonstrate a concrete application of our main results arising from the dynamic thermoviscoelasticity problems.
We consider a nonautonomous (
p
,
q
)-equation with unbalanced growth and a reaction which exhibits the combined effects of a parametric “concave" (
(
p
-
1
)
-sublinear) term and of a
(
p
-
1
)
...-linear perturbation, which asymptotically stays above the principal eigenvalue
λ
^
1
a
>
0
of the Dirichlet
-
Δ
p
a
operator. Using variational tools, truncation and comparison techniques and critical groups, we show that for all small values of the parameter the problem has at least three nontrivial bounded solutions with sign information (positive, negative, nodal), which are ordered.
Nodal solutions for (p,2)-equations AIZICOVICI, SERGIU; PAPAGEORGIOU, NIKOLAOS S.; STAICU, VASILE
Transactions of the American Mathematical Society,
10/2015, Letnik:
367, Številka:
10
Journal Article
Recenzirano
Odprti dostop
-(sub-)linear reaction. Using variational methods combined with Morse theory, we prove two multiplicity theorems providing precise sign information for all the solutions (constant sign and nodal ...solutions). In the process, we prove two auxiliary results of independent interest.>
In the present paper, we are concerned with the study of a variable exponent double-phase obstacle problem which involves a nonlinear and nonhomogeneous partial differential operator, a multivalued ...convection term, a general multivalued boundary condition and an obstacle constraint. Under the framework of anisotropic Musielak–Orlicz Sobolev spaces, we establish the nonemptiness, boundedness and closedness of the solution set of such problems by applying a surjectivity theorem for multivalued pseudomonotone operators and the variational characterization of the first eigenvalue of the Steklov eigenvalue problem for the
p
-Laplacian. In the second part, we consider a nonlinear inverse problem which is formulated by a regularized optimal control problem to identify the discontinuous parameters for the variable exponent double-phase obstacle problem. We then introduce the parameter-to-solution map, study a continuous result of Kuratowski type and prove the solvability of the inverse problem.
We consider a nonlinear eigenvalue problem for the Dirichlet (p,q)$(p,q)$‐Laplacian with a sign‐changing Carathé$\acute{\rm e}$odory reaction. Using variational tools, truncation and comparison ...techniques, and critical groups, we prove an existence and multiplicity result which is global in the parameter λ>0$\lambda >0$ (bifurcation‐type theorem). Our work here complements the recent one by Papageorgiou–Qin–Rădulescu, Bull. Sci. Math. 172 (2021).
We consider a parametric nonlinear Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p,2)-equation) and with a reaction which has the competing effects of two distinct ...nonlinearities. A parametric term which is (p−1)-superlinear (convex term) and a perturbation which is (p−1)-sublinear (concave term). First we show that for all small values of the parameter the problem has at least five nontrivial smooth solutions, all with sign information. Then by strengthening the regularity of the two nonlinearities we produce two more nodal solutions, for a total of seven nontrivial smooth solutions all with sign informations. Our proofs use critical point theory, critical groups and flow invariance arguments.
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