Existence results for a class of semilinear degenerate elliptic equations

Salvatore Bonafede

Mathematica Bohemica (2003)

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

Abstract

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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.

How to cite

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Bonafede, 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

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  1. Sobolev Spaces, Academic Press, New York, 1975. (1975) Zbl0314.46030MR0450957
  2. Critical points and nonlinear variational problems, Mem. Soc. Math. France 49 (1992). (1992) Zbl0766.49006MR1164129
  3. Quasilinear degenerate elliptic variational inequalities with discontinuous coefficients, Comment. Math. Univ. Carolin. 34 (1993), 55–61. (1993) Zbl0823.35067MR1240203
  4. A weak maximum principle and estimates of ess sup Ω u for nonlinear degenerate elliptic equations, Czechoslovak Math. J. 121 (1996), 259–269. (1996) MR1388615
  5. Quasilinear Elliptic Equations with Degenerations and Singularities De Gruyter Series in Nonlinear Analysis and Applications, New York, 1997, . MR1460729
  6. W -solutions of boundary value problems for degenerate elliptic operators, Ricerche di Matematica Suppl. 36 (1987), 59–72. (1987) MR0956018
  7. Existence theorems for boundary value problems associated with quasilinear elliptic equations, Ricerche di Matematica 37 (1988), 157–176. (1988) MR1021963
  8. 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. 
  9. Linear and Quasilinear Elliptic Equations, Academic Press, New York, 1968. (1968) MR0244627
  10. 10.1007/BF02413623, Ann. Mat. Pura Appl. 80 (1968), 1–122. (1968) MR0249828DOI10.1007/BF02413623
  11. Le probleme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus, Annal. Inst. Fourier 15 (1965), 187–257. (1965) Zbl0151.15401MR0192177
  12. Teoremi di inclusione per spazi di Sobolev non isotropi, Ricerche Mat. 18 (1989), 3–24. (1989) MR0415302

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