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weak subsolution; degenerate equation; critical point; fixed-point theorems
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.
[1] Adams, R. A.: Sobolev Spaces. Academic Press, New York, 1975. MR 0450957 | Zbl 0314.46030
[2] Ambrosetti, A.: Critical points and nonlinear variational problems. Mem. Soc. Math. France 49 (1992). MR 1164129 | Zbl 0766.49006
[3] Bonafede, S.: Quasilinear degenerate elliptic variational inequalities with discontinuous coefficients. Comment. Math. Univ. Carolin. 34 (1993), 55–61. MR 1240203 | Zbl 0823.35067
[4] Bonafede, S.: A weak maximum principle and estimates of $\text{ess}\,\text{sup}_{\Omega } u$ for nonlinear degenerate elliptic equations. Czechoslovak Math. J. 121 (1996), 259–269. MR 1388615
[5] Drábek, P., Kufner, A., Nicolosi, F.: Quasilinear Elliptic Equations with Degenerations and Singularities De Gruyter Series in Nonlinear Analysis and Applications, New York, 1997. MR 1460729
[6] Guglielmino, F., Nicolosi, F.: $W$-solutions of boundary value problems for degenerate elliptic operators. Ricerche di Matematica Suppl. 36 (1987), 59–72. MR 0956018
[7] Guglielmino, F., Nicolosi, F.: Existence theorems for boundary value problems associated with quasilinear elliptic equations. Ricerche di Matematica 37 (1988), 157–176. MR 1021963
[8] Ivanov, A. V., Mkrtycjan, P. Z.: 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] Ladyzenskaja, O. A., Ural’tseva, N. N.: Linear and Quasilinear Elliptic Equations. Academic Press, New York, 1968. MR 0244627
[10] Murthy, M. K. V., Stampacchia, G.: Boundary value problems for some degenerate-elliptic operators. Ann. Mat. Pura Appl. 80 (1968), 1–122. DOI 10.1007/BF02413623 | MR 0249828
[11] Stampacchia, G.: Le probleme de Dirichlet pour les equations elliptiques du second ordre a coefficients discontinus. Annal. Inst. Fourier 15 (1965), 187–257. MR 0192177 | Zbl 0151.15401
[12] Troisi, M.: Teoremi di inclusione per spazi di Sobolev non isotropi. Ricerche Mat. 18 (1989), 3–24. MR 0415302
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