On some nonlinear singular boundary value problems of higher order

Nonlinear Analysis, Theory, Methods and Applications

Volumn 26, Issue 6, 1996, Pages 1061-1078

  Bernis, Francisco ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Asymptotic behaviour; Boundary value problem; Degenerate parabolic equations; Existence; Nonexistence; Nonlinear; Singular; Uniqueness

Indexed keywords

EID: 0007144764     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00263-H     Document Type: Article

References (26)

1. BERTOZZI A. L., BRENNER M. P., DUPONT T. F. & KADANOFF L. P., Singularities and similarities in interface flows, In Applied Mathematics Series Centennial Volume (Edited by L. SIROVICH). Springer-Verlag, Berlin (1994).
2. BOATTO S., KADANOFF L. P. & OLLA P., Traveling-wave solutions to thin-film equations, Phys. Rev. Lett. E 48, 4423-4431 (1993).
3. GREENSPAN H. P., On the motion of a small viscous droplet that wets a surface, J. Fluid Mech 84, 125-143 (1978).
4. GREENSPAN H. P. & McCAY B.M., On the wetting of a surface by a very viscous fluid, Stud. appl. Math. 64, 95-112 (1981).
5. HOCKING L. M., Sliding and spreading of thin two-dimensional drops, Q. J. Mech. Appl. Math. 34, 37-55 (1981).
6. HOCKING L. M., The spreading of a thin drop by gravity and capillarity, Q. J. Mech. Appl. Math. 36, 55-69 (1983).
7. LACEY A. A., The motion with slip of a thin viscous droplet over a solid surface, Stud. appl. Math. 67, 217-230 (1982).
8. BERNIS F., PELETIER L. A., & WILLIAMS S. M., Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlinear Analysis 18, 217-234 (1992).
9. KING J. R., The isolation oxidation of silicon: the reaction-controlled case, SIAM J. Appl. Math. 49, 1064-1080 (1989).
10. TAYLER A. B. & KING J. R., Free boundaries in semi-conductor fabrication. In Free Boundary Problems: Theory and Applications (Edited by K. H. HOFFMAN & J. SPREKELS), Vol. I, pp, 243-259. Pitman Research Notes in Mathematics 185, Longman, Harlow (1990).
11. BERNIS F., Nonlinear parabolic equations arising in semiconductor and viscous droplets models. In Nonlinear Diffusion Equations and their Equilibrium States (Edited by N. G. LLOYD, W.-M. NI, L. A. PELETIER & J. SERRIN), pp. 77-88. Birkhäuser, Boston (1992).
12. SMYTH N. F. & HILL J. M., High-order nonlinear diffusion, IMA J. Appl. math. 40, 73-86 (1988)
13. CALLEGARI A. & NACHMAN A., Some singular, nonlinear differential equations arising in boundary layer theory, J. math. Analysis Applic. 64 96-105 (1978)
14. CALLEGARI A. & REISS E., Nonlinear boundary value problems for circular membranes, Archs ration. Mech. Analysis 31, 390-400 (1968)
15. DUNNINGER D. R. & KURTZ J. C., A priori bounds and existence of positive solutions for singular nonlinear boundary value problems, SIAM J. math. Analysis 17, 595-609 (1986).
16. LUNING C. D. & PERRY W. L., Positive solutions of negative exponent generalized Emden-Fowler boundary value problems, SIAM J. math. Analysis 12, 874-879 (1981)
17. O'REGAN D., Existence of positive solutions to some singular and nonsingular second order boundary value problems, J. diff. Eqns 84, 228-251 (1990)
18. O'REGAN D., Singular Sturm-Liouville problems and existence of solutions to singular nonlinear boundary value problems, Nonlinear Analysis 20, 767-779 (1993)
19. TALIAFERRO S. D., A nonlinear singular boundary value problem, Nonlinear Analysis 3, 897-904 (1979)
20. FULKS W. & MAYBEE J. S., A singular nonlinear equation, Osaka Math. J. 12, 1-19 (1960)
21. COCLITE M. M. & PALMIERI A., On a singular nonlinear Dirichlet problem, Communs. partial diff. Eqns 14, 1315-1327 (1989)
22. CRANDALL M. G., RABINOWITZ P. H. & TARTAR L., On a Dirichlet problem with a singular nonlinearity, Communs. partial diff. Eqns 2, 193-222 (1977)
23. O'REGAN D., Singular third-order boundary value problems, Diff. Integral Eqns 4, 1391-1417 (1991)
24. O'REGAN D., Solvability of some fourth (and higher) order singular boundary value problems, J. math. Analysis Applic. 161, 78-116 (1991)
25. O'REGAN D., Solvability of some second and higher order boundary value problems. Nonlinear Analysis 16, 507-516 (1991)
26. STAKGOLD I., Green's Functions and Boundary Value Problems. John Wiley & Sons (1979)