Infinite dimensional non-symmetric Borsuk-Ulam theorem
Infinitely many positive solutions for the Neumann problem involving the p-Laplacian
We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, with and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.
Infinitely many solutions for a semilinear elliptic equation in via a perturbation method
We introduce a method to treat a semilinear elliptic equation in (see equation (1) below). This method is of a perturbative nature. It permits us to skip the problem of lack of compactness of but requires an oscillatory behavior of the potential b.
Infinitely many solutions of a second-order -Laplacian problem with impulsive condition
Using the critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a -Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the -Laplacian impulsive problem.
Inflated mappings for singularities of codimension
Injectivity onto a star-shaped set for local homeomorphisms in n-space
We provide a number of either necessary and sufficient or only sufficient conditions on a local homeomorphism defined on an open, connected subset of the n-space to be actually a homeomorphism onto a star-shaped set. The unifying idea is the existence of "auxiliary" scalar functions that enjoy special behaviours along the paths that result from lifting the half-lines that radiate from a point in the codomain space. In our main result this special behaviour is monotonicity, and the auxiliary function...
Instability of Turing type for a reaction-diffusion system with unilateral obstacles modeled by variational inequalities
We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters...
Integrable solutions of a functional-integral equation.
This paper contains a theorem on the existence of monotonic and integrable solutions of a functional-integral equation. The proof of that theorem is based on the technique associated with the notion of a measure of weak noncompactness.
Integral control of infinite-dimensional systems in the presence of hysteresis: an input-output approach
This paper is concerned with integral control of systems with hysteresis. Using an input-output approach, it is shown that application of integral control to the series interconnection of either (a) a hysteretic input nonlinearity, an L2-stable, time-invariant linear system and a non-decreasing globally Lipschitz static output nonlinearity, or (b) an L2-stable, time-invariant linear system and a hysteretic output nonlinearity, guarantees, under certain assumptions, tracking of constant reference...
Interaction of Periodic and Stationary Bifurcation from Multiple Eigenvalues.
Interior proximal method for variational inequalities on non-polyhedral sets
Interior proximal methods for variational inequalities are, in fact, designed to handle problems on polyhedral convex sets or balls, only. Using a slightly modified concept of Bregman functions, we suggest an interior proximal method for solving variational inequalities (with maximal monotone operators) on convex, in general non-polyhedral sets, including in particular the case in which the set is described by a system of linear as well as strictly convex constraints. The convergence analysis of...
Inverse differentiability contractors and equations in Banach spaces
Inverse function theorems for Banach spaces in a topos
Inverse rate-dependent Prandtl-Ishlinskii operators and applications
In the past years, we observed an increased interest in rate-dependent hysteresis models to characterize complex time-dependent nonlinearities in smart actuators. A natural way to include rate-dependence to the Prandtl-Ishlinskii model is to consider it as a linear combination of play operators whose thresholds are functions of time. In this work, we propose the extension of the class of rate-dependent Prandtl-Ishlinskii operators to the case of a whole continuum of play operators with time-dependent...
Inversion of multifunctions and differential inclusions
Inverting the p-harmonic operator.
Ishikawa iteration process with errors for nonexpansive mappings.
Ishikawa iteration process with errors for nonexpansive mappings in uniformly convex Banach spaces.
Ishikawa iterative process for a pair of single-valued and multivalued nonexpansive mappings in Banach spaces.
Ishikawa iterative process with errors for generalized Lipschitzian and Phi-accretive mappings in uniformly smooth Banach spaces