Steady state solutions of diffusion-reaction systems with electrostatic convection. (English) Zbl 0438.35030


35J65 Nonlinear boundary value problems for linear elliptic equations
35B50 Maximum principles in context of PDEs
76R05 Forced convection
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[1] Amann, H., On the existence of positive solutions of nonlinear elliptic boundary valueproblems, Indiana univ. math. J., 21, 125-146, (1971) · Zbl 0219.35037
[2] Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM rev., 18, 620-709, (1976) · Zbl 0345.47044
[3] Aris, R., The mathematical theory of diffusion and reaction in permeable catalysts, (1975), Clarendon Press Oxford, (Two volumes), · Zbl 0315.76051
[4] Choo, S.C.; Seidman, T.I., Iterative scheme for computer simulation of semiconductor devices, Solid-state electronics, 15, 1229-1235, (1972)
[5] Deuel, J.; Hess, P., A criterion for the existence of solutions of nonlinear elliptic boundary value problems, Proc. R. soc. Edinburgh, 74A, 49-54, (1975) · Zbl 0331.35028
[6] Hess, P., On a second-order nonlinear elliptic boundary value problem, (), 99-107
[7] Mock, M.S., On equations describing steady-state carrier distributions in a semiconductor device, Communs. pure appl. math., XXV, 781-792, (1972)
[8] Morrey, C., Multiple integrals in the calculus of variations, (1966), Springer-Verlag New York · Zbl 0142.38701
[9] Nichols, K.G.; Vernon, E., Transistor physics., (1966), Chapman and Hall London
[10] Sattinger, D.H., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana univ. math. J., 21, 979-1000, (1972) · Zbl 0223.35038
[11] Seeger, K., Semiconductor physics, (1973), Springer-Verlag New York
[12] Seidman, T.I., On 2nd order quasilinear elliptic and parabolic equations with an application to diffusion-convection systems arising in semiconductor theory, (), 67
[13] Stampacchia, G., Équations elliptiques du 2-me ordre à coefficients discontinues, (1965), Les Presses de l’Univ. de Montréal
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