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MSC: 35J05, 78A40. Keywords: Helmholtz equation, wave-guide, periodic media,Fredholm alternative. 1 Introduction. ... Our result has therefore verymuch the character of a Fredholm alternative: If solutions are unique, then theyexist for arbitrary f.

problem. without a lower bound on c. Proposition 3.3 (Fredholm alternative). Suppose that the hypotheses of Propo-sition 3.2 hold, then either the homogeneous problem. ... ut. The Fredholm alternative in Proposition 3.3 then gives the main theorem of

Meury 3. Fredholm alternative. To this end, most authors have studied the integral operators intrinsicallyon Γ. ... Fredholm alternative on either smooth or non-smooth domainsand prevents us from establishing existence and uniqueness of solutions and

Instead, we show belowthat aω satisfies a G̊arding’s inequality. Then, according to Fredholm’s alternative,uniqueness implies existence of solution. ... Because of Lemma 3.2 we knowthat the problem satisfies Fredholm’s alternative (see for

In particular, we identify the Fredholm deter-minant of the integral equation inverting the nonlocal ̄-dressing problem with the τ -function. ... Then, by the Fredholm alternative, the homogeneousequation with η = 0 has only the trivial solution.

We require the following lemmawhich is a simple case of the Fredholm Alternative Theorem (see, for example, [22]) and leave thedetails for the reader:.

STABILITY OF THE PERIODIC TODA LATTICE. UNDER SHORT RANGE PERTURBATIONS. SPYRIDON KAMVISSIS AND GERALD TESCHL. Abstract. We consider the stability of the periodic Toda lat-tice (and slightly more generally of the algebro-geometric finite-gap lattice)

SPECTRA OF GRAPH NEIGHBORHOODS AND SCATTERING. DANIEL GRIESER. Abstract. Let (Gε)ε>0 be a family of ’ε-thin’ Riemannian manifolds modeledon a finite metric graph G, for example, the ε-neighborhood of an embeddingof G in some Euclidean space