Maximum principles for fourth order semilinear elliptic boundary value problems
Downloads
DOI:
https://doi.org/10.26637/mjm103/007Abstract
The paper is devoted to prove maximum principles for the certain functionals defined on solution of the fourth order semilinear elliptic equation. The maximum principle so obtained is used to prove the non-existence of nontrivial solutions of the fourth order semilinear elliptic equation with some zero boundary conditions. Hopf’s maximum principle is main ingredient.
Keywords:
Maximum principles, fourth order elliptic equations, integral boundsMathematics Subject Classification:
35J40, 35J61- Pages: 44-48
- Date Published: 01-07-2013
- Vol. 1 No. 03 (2013): Malaya Journal of Matematik (MJM)
D. B. Dhaigude, Comparison theorems for a class of elliptic equations of order 4 m, Chinese J. Math., 15(1987), 61-67.
D. B. Dhaigude and D. Y. Kasture, Comparison theorems for nonlinear elliptic systems of second order with applications, J. Math. Anal. Appl., 112(1985), 178-189. DOI: https://doi.org/10.1016/0022-247X(85)90284-7
D. B. Dhaigude and M. R. Gosavi, Maximum principles for fourth order semilinear elliptic equations and applications, Differ. Equ. Dyn. Syst., 12:3(4)(2004), 279-287.
D. R. Dunninger, Maximum principles for solutions of some fourth- order elliptic equations, J. Math.Anal. Appl., 37(1972), 655-658. DOI: https://doi.org/10.1016/0022-247X(72)90248-X
C. Miranda, Formule di maggiorazione e teorema di esistenza per le funzioni biarmoniche di due variabli, Giorn. Mat. Battaglini, 78(1948), 97-118.
M. H. Protter and H. F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, New York, 1984. DOI: https://doi.org/10.1007/978-1-4612-5282-5
P. W. Schaefer, On a maximum principle for a class of fourth order semilinear elliptic equations, Proc. Roy. Soc., 77A(1977), 319-323. DOI: https://doi.org/10.1017/S0308210500025233
R. P. Sperb, Maximum Principles and Their Applications, Academic Press, New York, 1981.
- NA
Similar Articles
- Rupali S. Jain, M. B. Dhakne, On mild solutions of nonlocal semilinear functional integro-differential equations , Malaya Journal of Matematik: Vol. 1 No. 03 (2013): Malaya Journal of Matematik (MJM)
You may also start an advanced similarity search for this article.
Metrics
Published
How to Cite
Issue
Section
License
Copyright (c) 2013 MJM
This work is licensed under a Creative Commons Attribution 4.0 International License.
