Geodesic
On the Dirichlet problem for a nonlinear elliptic equation
Sbornik. Mathematics, Tome 206 (2015) no. 4, pp. 480-488 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove the existence of an infinite set of solutions to the Dirichlet problem for a nonlinear elliptic equation of the second order. Such a problem for a nonlinear elliptic equation with Laplace operator was studied earlier by Krasnosel'skii, Bahri, Berestycki, Lions, Rabinowitz, Struwe and others. We study the spectrum of this problem and prove the weak convergence to 0 of the sequence of normed eigenfunctions. Moreover, we obtain some estimates for the ‘Fourier coefficients’ of functions in $W^1_{p,0}(\Omega)$. This allows us to improve the preceding results. Bibliography: 8 titles.
Keywords: nonlinear elliptic equation, Dirichlet problem, eigenfunctions. 
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Yu. V. Egorov. On the Dirichlet problem for a nonlinear elliptic equation. Sbornik. Mathematics, Tome 206 (2015) no. 4, pp. 480-488. http://geodesic.mathdoc.fr/item/SM_2015_206_4_a0/

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