# Existence results for a class of semilinear degenerate elliptic equations

Mathematica Bohemica (2003)

- Volume: 128, Issue: 2, page 187-198
- ISSN: 0862-7959

## Access Full Article

top## Abstract

top## How to cite

topBonafede, Salvatore. "Existence results for a class of semilinear degenerate elliptic equations." Mathematica Bohemica 128.2 (2003): 187-198. <http://eudml.org/doc/249226>.

@article{Bonafede2003,

abstract = {We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.},

author = {Bonafede, Salvatore},

journal = {Mathematica Bohemica},

keywords = {weak subsolution; degenerate equation; critical point; fixed-point theorems; weak subsolution; degenerate equation; critical point; fixed-point theorems},

language = {eng},

number = {2},

pages = {187-198},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Existence results for a class of semilinear degenerate elliptic equations},

url = {http://eudml.org/doc/249226},

volume = {128},

year = {2003},

}

TY - JOUR

AU - Bonafede, Salvatore

TI - Existence results for a class of semilinear degenerate elliptic equations

JO - Mathematica Bohemica

PY - 2003

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 128

IS - 2

SP - 187

EP - 198

AB - We prove existence results for the Dirichlet problem associated with an elliptic semilinear second-order equation of divergence form. Degeneracy in the ellipticity condition is allowed.

LA - eng

KW - weak subsolution; degenerate equation; critical point; fixed-point theorems; weak subsolution; degenerate equation; critical point; fixed-point theorems

UR - http://eudml.org/doc/249226

ER -

## References

top- Sobolev Spaces, Academic Press, New York, 1975. (1975) Zbl0314.46030MR0450957
- Critical points and nonlinear variational problems, Mem. Soc. Math. France 49 (1992). (1992) Zbl0766.49006MR1164129
- Quasilinear degenerate elliptic variational inequalities with discontinuous coefficients, Comment. Math. Univ. Carolin. 34 (1993), 55–61. (1993) Zbl0823.35067MR1240203
- A weak maximum principle and estimates of $\text{ess}\phantom{\rule{0.166667em}{0ex}}{\text{sup}}_{\Omega}u$ for nonlinear degenerate elliptic equations, Czechoslovak Math. J. 121 (1996), 259–269. (1996) MR1388615
- Quasilinear Elliptic Equations with Degenerations and Singularities De Gruyter Series in Nonlinear Analysis and Applications, New York, 1997, . MR1460729
- $W$-solutions of boundary value problems for degenerate elliptic operators, Ricerche di Matematica Suppl. 36 (1987), 59–72. (1987) MR0956018
- Existence theorems for boundary value problems associated with quasilinear elliptic equations, Ricerche di Matematica 37 (1988), 157–176. (1988) MR1021963
- On the solvability of the first boundary value problem for certain classes of degenerating quasilinear elliptic equations of second order, Boundary value problems of mathematical physics, O. A. Ladyzenskaja (ed.), Vol. 10, Proceedings of the Steklov Institute of Mathematics, A.M.S. Providence (1981, issue 2), pp. 11–35.
- Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. (1968) MR0244627
- 10.1007/BF02413623, Ann. Mat. Pura Appl. 80 (1968), 1–122. (1968) MR0249828DOI10.1007/BF02413623
- Le probleme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus, Annal. Inst. Fourier 15 (1965), 187–257. (1965) Zbl0151.15401MR0192177
- Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat. 18 (1989), 3–24. (1989) MR0415302

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.