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Therefore, our existence proof mainly relies on a simple fixed point iterationand standard Fredholm theory. ... u Ku = L1T f. Since 1l K is a Fredholm operator, the second equation has a solution if and only if(1l K)u = 0 implies u = 0.

Existence results for the. Helmholtz equation in periodic. wave-guides with energy methods. ... MSC: 35J05, 78A40. Keywords: Helmholtz equation, wave-guide, periodic media,Fredholm alternative. 1 Introduction.

26 Jul 2013: Although our equivalent to an equation. of state is too complicated to show a simple relationship between. ... Eqn (21) is a well-posed. Fredholm integral equation of the second kind for the unknown.

25 Jan 2007: The sine-Gordon equation appears in a variety of geometrical and physical applications. ... where C is the unit circle.This equation can be solved in closed form because the Fredholm kernel (tt1)(τ τ 1) is degenerate:.

the Fredholm module canonically associated to the spectral triple to an ‘instanton’ projection e. ... With different representations a non-trivial Fredholm module was already constructed in [17].

the elliptic background, such as the nonlinear dispersion relations (NDR) and the equation of state. ... equation (NLS) and KdV can be found in [9, 7], see also [8], [24].

23 Sep 2020: Suchboundary conditions, namely the varying physicalparameters and coupled thin-plate equation, presenta considerable challenge to current methods. ... and difficult due to the need to solve a matrix, rather than ascalar, Wiener–Hopf equation.

2; Rn) (see Section 5 for the definition of this space) of equation. ... only strong solution to equation (13)and ΛU is as in Theorem 7).

27 Apr 2019: ds = 0, (2.6). where v is any solution to the (adjoint) Helmholtz equation. ... Choosing the Green’s function that satisfies ahomogeneous Dirichlet boundary condition on the x-axis, the boundary integral equations giverise to the following Fredholm

10 Apr 2011: x2 x8!21 h x!2 h x8! 2,. 6! where the vortex sheet strengthg satisfies a Fredholm integral equation of the second kindg 1 2AmŪ@ g #• 1,hx! ... h̄ can be scaled out of the equation, but we did ndo so!