Geodesic
The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 15-27 Cet article a éte moissonné depuis la source Math-Net.Ru

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For mixed type equation $$ Lu\equiv u_{xx}+sgny\cdot |y|^m u_{yy}=0,\: 01\nonumber $$ \noindent in a rectangular domain $\{(x,y)|\quad 0$, where $m,\alpha,\beta$ – defined positive numbers, theorems of existence and uniqueness of the problem solvability with boundary solutions $u(0,y)=u(1,y)$, $u_x(0,y)=u_x(1,y)$, $-\alpha\leq y\leq \beta$; $u(x,\beta)=f(x)$, $u(x,-\alpha)=g(x),$ $0\le x\le 1$ are proved by the method of spectral analysis.
Keywords: eigenfunctions, spectral analysis. 
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     author = {I. P. Egorova},
     title = {The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy},
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I. P. Egorova. The problem with periodicity conditions for the equations of mixed type with characteristic degeneracy. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 8 (2009), pp. 15-27. http://geodesic.mathdoc.fr/item/VSGU_2009_8_a1/

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