Geodesic
On the asymptotic properties and necessary conditions for existence of solutions of nonlinear second order elliptic equations
Sbornik. Mathematics, Tome 35 (1979) no. 6, pp. 823-849 
I. Kametaka; O. A. Oleinik. On the asymptotic properties and necessary conditions for existence of solutions of nonlinear second order elliptic equations. Sbornik. Mathematics, Tome 35 (1979) no. 6, pp. 823-849. http://geodesic.mathdoc.fr/item/SM_1979_35_6_a3/
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     title = {On the asymptotic properties and necessary conditions for existence of solutions of nonlinear second order elliptic equations},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1979_35_6_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper functions $u(x)$ satisfying the inequality $L(u)+k(x)f(u)\leqslant0$ in a domain $\Omega$ are studied. Here $L(u)$ is a linear second order elliptic operator with positive definite characteristic form, $k(x)\geqslant0$, and $f(u)$ is defined in an interval $u^-, in which $f(u)>0$, $f'(u)\geqslant0$ and $\int_u^{u^+}\frac{ds}{f(s)}<\infty$. Bibliography: 13 titles.

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[3] S. I. Pokhozhaev, “O zadache Dirikhle dlya uravneniya $\Delta u=u^2$”, DAN SSSR, 134:4 (1960), 769–772 | Zbl

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[6] O. A. Oleinik, “Ob uravnenii $\Delta u+k(x)e^u=0$”, Uspekhi matem. nauk, XXXIII:2(200) (1978), 203–204 | MR

[7] H. Fujita, “On the blowing up of solutions of the Cauchy problem for $u_t=\Delta u+u^{1+\alpha}$”, J. Fac. Sci. Univ. Tokyo, Sect. 1, 13 (1966) | MR | Zbl

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[10] J. L. Kazdan, F. W. Warner, “Remarks on some quasilinear elliptic equations”, Comm. Pure and Appl. Math., 28 (1975), 567–597 | DOI | MR | Zbl

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