Geodesic
On the Equation $\Delta u+q(x)u=0$
Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 101-109

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Sufficient conditions for the blow-up of nontrivial generalized solutions of the interior Dirichlet problem with homogeneous boundary condition for the homogeneous elliptic-type equation $\Delta u+q(x)u=0$, where either $q(x)\ne\mathrm{const}$ or $q(x)=\mathrm{const}=\lambda>0$, are obtained. A priori upper bounds (Theorem 4 and Remark 6) for the exact constants in the well-known Sobolev and Steklov inequalities are established.
Keywords: generalized solution, Dirichlet problem, Sobolev inequality, Steklov inequality
Mots-clés : Fourier transform. 
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     author = {Sh. M. Nasibov},
     title = {On the {Equation} $\Delta u+q(x)u=0$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {101--109},
     publisher = {mathdoc},
     volume = {101},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a8/}
}
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Sh. M. Nasibov. On the Equation $\Delta u+q(x)u=0$. Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 101-109. http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a8/