论文信息 - On a class of nonlocal nonlinear elliptic problems

On a class of nonlocal nonlinear elliptic problems

We give a direct approach to the solvability of a class of nonlocal problems which admit a formulation in terms of quasi- variational inequalities. We are motivated by nonlinear elliptic boundary value problems in which certain coefficients depend, in a rather general way, on the solution itself through global quantities like the total mass, the total flux or the total energy. We illustrate the existence results with several applications, including an implicit Signorini problem for steady diffusion of biological populations and a class of operator equations in nonlinear mechanics. We also discuss the non- uniqueness of the solutions.

Michel Chipot | José Francisco Rodrigues | J. Rodrigues | M. Chipot

[1] D. Gilbarg,et al. Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[2] D. Kinderlehrer,et al. An introduction to variational inequalities and their applications , 1980 .

[3] Morton E. Gurtin,et al. On the diffusion of biological populations , 1977 .

[4] J. Lions,et al. Quelques résultats de Višik sur les problèmes elliptiques non linéaires par les méthodes de Minty-Browder , 1964 .

[5] J. Lions. Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[6] A. Bensoussan,et al. Contrôle impulsionnel et inéquations quasi variationnelles , 1982 .

[7] J. Rodrigues. Obstacle Problems in Mathematical Physics , 1987 .

[8] Jindřich Nečas,et al. Introduction to the Theory of Nonlinear Elliptic Equations , 1986 .

[9] J. Eisley. Nonlinear vibration of beams and rectangular plates , 1964 .

[10] H. Brezis. Analyse fonctionnelle : théorie et applications , 1983 .

[11] Jean-Luc Joly,et al. A propos de l'existence et de la régularité des solutions de certaines inéquations quasi-variationnelles , 1979 .

[12] U. Mosco. Implicit variational problems and quasi variational inequalities , 1976 .

[13] L. A. Medeiros,et al. On a New Class of Nonlinear Wave Equations , 1979 .