×

zbMATH — the first resource for mathematics

Boundary value problems on infinite intervals and semiconductor devices. (English) Zbl 0594.34019
Summary: The nonlinear differential equation \(y''=f(x,y,y')\), \(0\leq x<\infty\) with appropriate boundary conditions is studied. Our treatment involves extending results of Granas, Guenther, and Lee concerning boundary value problems on finite intervals with f satisfying Bernstein type growth conditions. We also examine an important application which occurs in the theory of semiconductor devices.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Berbernes, J.W.; Jackson, L.K., Infinite interval boundary value problems for y″ = f(x, y), Duke math. J., 34, 39-47, (1967) · Zbl 0145.33102
[2] Buturla, E.M.; Cottrell, P.E.; Grossman, B.M.; Salsburg, K.A., Finite-elements analysis of semiconductor devices: the FIELDAY program, IBM J. res. dev., 24, 218-231, (1981)
[3] Kim, Choong-Ki, The physics of charge coupled devices, ()
[4] Dugundji, J.; Granas, A., Fixed point theory, Vol. 1, (1982), Monografie Mathematyczne, Warsaw · Zbl 0483.47038
[5] Granas, A.; Guenther, R.B.; lee, J.W., On a theorem of S. Bernstein, Pacific J. math., 74, 67-82, (1978) · Zbl 0377.34003
[6] Granas, A.; Guenther, R.B.; Lee, J.W., Nonlinear boundary value problems for some classes of ordinary differential equations, Rocky mountain J. math., 10, 35-58, (1980) · Zbl 0476.34017
[7] Granas, A.; Guenther, R.B.; Lee, J.W., Topological transversality, II, applications to the Neumann problem for y″ = f(t, y, y′), Pacific J. math., 104, 95-109, (1983) · Zbl 0534.34006
[8] Granas, A.; Guenther, R.B.; Lee, J.W., Topological transversality. I. some nonlinear diffusion problems, Pacific J. math., 89, 53-67, (1980) · Zbl 0453.34018
[9] Spenke, E., Elektronische halbleiter, eine einführung in die physik der gleichrichter und transistoren, (1965), Springer-Verlag New York · Zbl 0064.23803
[10] Sze, S.M., Physics of semiconductor devices, (1969), Wiley-Interscience Berlin
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.