Geodesic
On sign variation and the absence of ``strong'' zeros of solutions of elliptic equations
Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 337-353

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The authors prove the existence of a convex domain $G$ with smooth boundary for which an eigenfunction corresponding to an eigenvalue of problem with operators of elliptic type is of variable sign. Bibliography: 10 titles. 
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     author = {V. A. Kozlov and V. A. Kondrat'ev and V. G. Maz'ya},
     title = {On sign variation and the absence of ``strong'' zeros of solutions of elliptic equations},
     journal = {Izvestiya. Mathematics },
     pages = {337--353},
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V. A. Kozlov; V. A. Kondrat'ev; V. G. Maz'ya. On sign variation and the absence of ``strong'' zeros of solutions of elliptic equations. Izvestiya. Mathematics , Tome 34 (1990) no. 2, pp. 337-353. http://geodesic.mathdoc.fr/item/IM2_1990_34_2_a5/