[Authors]
 Ustinov, N. S.

[Title]
 Multiplicity of positive solutions to the boundary value problems
 for fractional Laplacians

[AMS Subj-class]
 35R11 Fractional partial differential equations
 35B06 Symmetries, invariants, etc.

[Abstract]
 We establish the so-called ``multiplicity effect'' for 
 the problem $(-\Delta)^s u= u^{q-1}$ in the annulus 
 $\Omega_R = B_{R+1}\setminus B_{R} \in \mathbb{R}^n$: 
 for each $N \in \mathbb{N}$ there exists $R_0$ such 
 that for all $R \geq R_0$ problem has $N$ different 
 positive solutions. $(-\Delta)^s$ in this problem 
 stands either for Navier-type or for Dirichlet-type 
 fractional Laplacian. Similar results were proved earlier 
 for the usual Laplace operator and for the $p$-Laplacian 
 operator.

[Comments]
 LaTeX, Russian, 17 pp.

[Contact e-mail]
 ustinns@yandex.ru