Geodesic
On the Dirichlet problem for a~nonlinear elliptic equation
Sbornik. Mathematics, Tome 206 (2015) no. 4, pp. 480-488

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_2015_206_4_a0,
     author = {Yu. V. Egorov},
     title = {On the {Dirichlet} problem for a~nonlinear elliptic equation},
     journal = {Sbornik. Mathematics},
     pages = {480--488},
     publisher = {mathdoc},
     volume = {206},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2015_206_4_a0/}
}
TY  - JOUR
AU  - Yu. V. Egorov
TI  - On the Dirichlet problem for a~nonlinear elliptic equation
JO  - Sbornik. Mathematics
PY  - 2015
SP  - 480
EP  - 488
VL  - 206
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2015_206_4_a0/
LA  - en
ID  - SM_2015_206_4_a0
ER  - 
%0 Journal Article
%A Yu. V. Egorov
%T On the Dirichlet problem for a~nonlinear elliptic equation
%J Sbornik. Mathematics
%D 2015
%P 480-488
%V 206
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2015_206_4_a0/
%G en
%F SM_2015_206_4_a0
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/