Geodesic
On some noncoercive nonlinear equations
Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 323-332 
Yu. A. Dubinskii. On some noncoercive nonlinear equations. Sbornik. Mathematics, Tome 16 (1972) no. 3, pp. 323-332. http://geodesic.mathdoc.fr/item/SM_1972_16_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper nonlinear equations $A(u)=h$ are studied, where the operator does not necessarily satisfy the well-known condition of coerciveness. With the equation $A(u)=h$, which is in general not solvable for an arbitrary right side $h$, we associate a certain equation of the form $B^*A(u)=h$, which is always solvable. Then the original equation $A(u)=h$ is solvable up to $\operatorname{Ker}B^*$. This gives a description of the domain of values of the original operator $A(u)$. Bibliography: 9 titles.

[1] J. Lions, Quelques methodes de resolution des problemes aux limites non linéaires, Paris, 1969

[2] F. E. Browder, Existence theorem for nonlinear partial differential equations, Preprint, 1969 | MR

[3] P. I. Kachurovskii, “Nelineinye monotonnye operatory v banakhovykh prostranstvakh”, Uspekhi matem. nauk, XXIII:2(140) (1968), 121–168

[4] Yu. A. Dubinskii, “Nelineinye ellipticheskie i parabolicheskie uravneniya vysokogo poryadka”, Uspekhi matem. nauk, XXIII:1(139) (1968), 45–90 | MR

[5] S. I. Pokhozhaev, “O nelineinykh operatorakh, imeyuschikh slabo zamknutuyu oblast znachenii, i kvazilineinykh ellipticheskikh uravneniyakh”, Matem. sb., 78(120) (1969), 237–259 | Zbl

[6] S. I. Pokhozhaev, “Normalnaya razreshimost nelineinykh uravnenii v ravnomerno vypuklykh banakhovykh prostranstvakh”, Funkts. analiz, 3:2 (1969), 80–84 | MR

[7] Yu. A. Dubinskii, “O razreshimosti v tselom nelineinykh obyknovennykh differentsialnykh uravnenii”, AN SSSR, 181:6 (1968), 1311–1313 | MR | Zbl

[8] S. L. Sobolev, Nekotorye primeneniya funktsionalnogo analiza v matematicheskoi fizike, Novosibirsk, 1962

[9] S. I. Pokhozhaev, “O sobstvennykh funktsiyakh kvazilineinykh ellipticheskikh zadach”, Matem. sb., 82(124) (1970), 192–212