Abstract
In this paper are given some sufficient conditions for validity of the comparison principle for linear and quasi-linear non-cooperative elliptic systems. Existence of classical solutions is proved as well.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
G. Boyadzhiev. Comparison principle for non-cooperative elliptic systems. Nonlinear Analysis, Theory, Methods and Applications, 69, (2008), no. 11, 3838–3848.
G. Boyadzhiev. Existence theorem for cooperative quasi-linear elliptic systems. C.R. Acad. Bulg. Sci., 63 (2010), no 9, 665–672.
G. Boyadzhiev. Existence of Classical Solutions of Linear Non-cooperative Elliptic Systems. C.R. Acad. Bulg. Sci., 68 (2015), no. (2), 159–164.
G. Boyadzhiev and N. Kutev. Existence of classical solutions of linear non - cooperative elliptic systems. Pliska Stud. Math.30 (2019), 45–54.
G. Caristi and E. Mitidieri. Further results on maximum principle for non-cooperative elliptic systems. Nonl.Anal.T.M.A., 17 (1991), 547–228.
L.C. Evans. (P)artial (D)ifferential (E)quations, series Graduate Studies in Mathematics, AMS, 1998.
D. Gilbarg and N. Trudinger. (E)lliptic (P)artial (D)ifferential (E)quations of (S)econd (O)rder. 2nd ed., Springer - Verlag, New York.
Li Jun Hei, Juan Hua Wu : Existence and Stability of Positive Solutions for an Elliptic Cooperative System. Acta Math. Sinica21 (2005), No 5, 1113–1130.
P. Hess. On the Eigenvalue Problem for Weakly Coupled Elliptic Systems, Arch. Ration. Mech. Anal.81 (1983), 151–159.
O.A. Ladyzhenskaya and N.Ural’tseva. (L)inear and (Q)uasilinear (E)quations of (E)lliptic (T)ype. Nauka, Moskwa, 1964.
O.A.Ladyzhenskaya, V. Rivkind and N. Ural’tseva. Classical solvability of diffraction problem for elliptic and parabolic equations with discontinuous coefficients. trudy Mat. Innst. Steklov, 92 (1996), 116–146. ( In Russian)
E. Mitidieri and G. Sweers. Weakly coupled elliptic systems and positivity. Math.Nachr.173 (1995), 259–286.
P. Popivanov. Explicit formulaes to the solutions of Dirichet problem for equations arising in geometry and physics. C.R.Acad.Bulg. Sci., 68 (2015), no 1, 19–24.
G. Sweers. A strong maximum principle for a noncooperative elliptic systems. SIAM J. Math. Anal., 20 (1989), 367–371.
G. Sweers. Strong positivity in \(C(\overline {\varOmega })\) for elliptic systems. Math.Z.209 (1992), 251–271.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Boyadzhiev, G., Kutev, N. (2020). Comparison Principle for Non-cooperative Elliptic Systems and Applications. In: Boggiatto, P., et al. Advances in Microlocal and Time-Frequency Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-36138-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-36138-9_8
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-36137-2
Online ISBN: 978-3-030-36138-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)