Generalized Spectrum of Second Order Differential Operators

On the Spectrum of a Class of Second Order Periodic Elliptic Differential Operators

On the spectrum of second order differential operators with complex coefficients

singular. Under the assumption that Imq(x) ≤ 0 for all x ∈ [a, b), Sims proved that for λ ∈ C+, there exists at least one solution of (1. 1) which lies in the weighted space L(a, b; Im[λ− q]dx); such a solution lies in L(a, b). There are now three distinct possibilities for λ ∈ C+: (I) there is, up to constant multiples, precisely one solution of (1. 1) in L(a, b; Im[λ−q]dx) and L(a, b), (II) o...

Fredholm properties of radially symmetric, second order differential operators

We analyze Fredholm properties of radially symmetric second order systems in unbounded domains. The main theorem relates the Fredholm index to the Morse index at infinity. As a consequence, linear operators are Fredholm in exponentially weighted spaces for almost all weights. The result provides the basic tool for the analysis of perturbation and bifurcation problems in the presence of essentia...

Differential Transformations of Parabolic Second-Order Operators in the Plane

The theory of transformations for hyperbolic second-order equations in the plane, developed by Darboux, Laplace and Moutard, has many applications in classical differential geometry [12, 13], and beyond it in the theory of integrable systems [14, 19]. These results, which were obtained for the linear case, can be applied to nonlinear Darboux-integrable equations [2, 7, 15, 16]. In the last deca...

Second order linear differential equations with generalized trapezoidal intuitionistic Fuzzy boundary value

In this paper the solution of a second order linear differential equations with intuitionistic fuzzy boundary value is described. It is discussed for two different cases: coefficient is positive crisp number and coefficient is negative crisp number. Here fuzzy numbers are taken as generalized trapezoidal intutionistic fuzzy numbers (GTrIFNs). Further a numerical example is illustrated.