Related papers: Bifurcation Theory for Fredholm Operators

We prove the invertibility of the relevant single and double layer potentials associated to some generalizations of the Stokes operator on bounded domains. In order to do that, we first develop an ``algebra tool kit'' to deal with limit and…

Based on operators borrowed from scattering theory, several concrete realizations of index theorems are proposed. The corresponding operators belong to some C*-algebras of pseudo-differential operators with coefficients which either have…

The index of a pseudo B-Fredholm operator will be defined and generalize the usual index of a B-Fredholm operator. This concept will be used to extend some known results in Fredholm's theory. Among other results, the nullity, the…

Muraleetharan and Thirulogasanthan in (J. Math. phys. 59, No. 10, 103506, 27p. (2018)) introduced the concept of Calkin Sspectrum of a bounded quaternionic linear operators. The study of this spectrum is establisched using the Fredholm…

The global bifurcation diagrams for two different one-parametric perturbations ($+\lambda x$ and $+\lambda x^2$) of a dissipative scalar nonautonomous ordinary differential equation $x'=f(t,x)$ are described assuming that 0 is a constant…

A celebrated result in bifurcation theory is that global connected sets of non-trivial solutions bifurcate from trivial solutions at non-zero eigenvalues of odd algebraic multiplicity of the linearized problem when the operators involved…

The Boutet de Monvel calculus of pseudo-differential boundary operators is generalised to the full scales of Besov and Triebel--Lizorkin spaces (though with finite integral exponents for the latter). The continuity and Fredholm properties…

We show a priori bounds for the dynamic fractional $\Phi^4$ model on $\mathbb{T}^3$ in the full subcritical regime using the framework of Hairer's regularity structures theory. Assuming the model bounds our estimates imply global existence…

Let $\alpha,\beta$ be orientation-preserving homeomorphisms of $[0,\infty]$ onto itself, which have only two fixed points at $0$ and $\infty$, and whose restrictions to $\mathbb{R}_+=(0,\infty)$ are diffeomorphisms, and let…

We establish Schauder a priori estimates and regularity for solutions to a class of boundary-degenerate elliptic linear second-order partial differential equations. Furthermore, given a smooth source function, we prove regularity of…

A regular elliptic boundary-value problem over a bounded domain with a smooth boundary is studied. We prove that the operator of this problem is a Fredholm one in the two-sided refined scale of the functional Hilbert spaces and generates a…

We investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove existence results by applying Schauder's fixed point technique. Moreover, we show fundamental…

This paper presents regularity results and associated high-order numerical methods for one-dimensional Fractional-Laplacian boundary-value problems. On the basis of a factorization of solutions as a product of a certain edge-singular weight…

We derive Fredholm determinant representation for isomonodromic tau functions of Fuchsian systems with $n$ regular singular points on the Riemann sphere and generic monodromy in $\mathrm{GL}(N,\mathbb C)$. The corresponding operator acts in…

This contribution extends the localized training approach, traditionally employed for multiscale problems and parameterized partial differential equations (PDEs) featuring locally heterogeneous coefficients, to the class of linear, positive…

Littlewood--Paley theory is a fundamental tool for frequency localization, square-function control, and multiplier analysis, yet a systematic counterpart in the fractional Fourier transform (FrFT) setting has remained incomplete. We develop…

We build a solvability theory of elliptic boundary-value problems in normed Sobolev spaces of generalized smoothness for any integrability exponent $p>1$. The smoothness is given by a number parameter and a supplementary function parameter…

We present an order-theoretical fixed point theorem for increasing multivalued operators suitable for the method of sub-supersolutions and its application to the following multivalued quasi-variational inclusion: Let $\Omega \subset \mathbb…

We consider elliptic second order partial differential operators with Lipschitz continuous leading order coefficients on finite cubes and the whole Euclidean space. We prove quantitative sampling and equidistribution theorems for…

We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…