A Rellich type identity and applications. (English) Zbl 0816.35027

The author develops Rellich’s idea to find general integral identities between pairs of smooth arbitrary functions in order to get non-existence results for semilinear elliptic systems and special classes of higher order equations. The relation of this paper to some previous results of Pohozaev and Pucci, Serrin should be pointed out.
Reviewer: P.Drábek (Plzeň)


35J60 Nonlinear elliptic equations
35J45 Systems of elliptic equations, general (MSC2000)
Full Text: DOI


[1] Clément Ph., to appear in Comm. P.D.E
[2] DOI: 10.1007/BF00381236 · Zbl 0724.35044
[3] Friedman A, I A, Math 34 pp 65– (1987)
[4] Mitidieri E., work in preparation
[5] Mitidieri E., preprint
[6] DOI: 10.1090/S0002-9947-1960-0111898-8
[7] Payne L.E, Pacific J. Math 8 pp 551– (1958)
[8] Peletier L.A., to appear in Diff. Integral Eqs
[9] Pohozaev S.I, Soviet Math.Dokl 5 pp 1408– (1965)
[10] DOI: 10.1512/iumj.1986.35.35036 · Zbl 0625.35027
[11] Pucci P, J Math. Pures et Appl 69 pp 55– (1990)
[12] DOI: 10.1007/BF01181459 · Zbl 0023.04204
[13] Van der Vorst R.C.A.M., preprint
[14] DOI: 10.1007/BF00375674 · Zbl 0796.35059
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