Geodesic
Existence results for non-autonomous elliptic boundary value problems
Electronic Journal of Differential Equations, Tome 1994 (1994) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study solutions to the boundary value problems $$\eqalign{-\Delta u(x) = \lambda f(x, u);\quad \ x \in \Omega\cr u(x) + \alpha(x) {\partial u(x)\over \partial n} = 0;\quad \ x \in \partial \Omega}$$ where $$\lambda \in (\lambda_{n}, \lambda_{n + 1})$$ where $\lambda_{k}$ is the k-th eigenvalue of $-\Delta$ subject to the above boundary conditions. In particular, one of the solutions we obtain has non-zero positive part, while another has non-zero negative part. We also discuss the existence of three solutions where one of them is positive, while another is negative, for $\lambda$ near $\lambda_{1}$, and for $\lambda$ large when f is sublinear. We use the method of sub-super solutions to establish our existence results. We further discuss non-existence results for $\lambda$ small.
Classification : 35J65
Keywords: elliptic boundary value problems, semipositone 
@article{EJDE_1994__1994_4_a0,
     author = {Anuradha, V. and Dickens, S. and Shivaji, R.},
     title = {Existence results for non-autonomous elliptic boundary value problems},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1994},
     number = {4},
     year = {1994},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1994__1994_4_a0/}
}
TY  - JOUR
AU  - Anuradha, V.
AU  - Dickens, S.
AU  - Shivaji, R.
TI  - Existence results for non-autonomous elliptic boundary value problems
JO  - Electronic Journal of Differential Equations
PY  - 1994
VL  - 1994
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_1994__1994_4_a0/
LA  - en
ID  - EJDE_1994__1994_4_a0
ER  - 
%0 Journal Article
%A Anuradha, V.
%A Dickens, S.
%A Shivaji, R.
%T Existence results for non-autonomous elliptic boundary value problems
%J Electronic Journal of Differential Equations
%D 1994
%V 1994
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_1994__1994_4_a0/
%G en
%F EJDE_1994__1994_4_a0
Anuradha, V.; Dickens, S.; Shivaji, R. Existence results for non-autonomous elliptic boundary value problems. Electronic Journal of Differential Equations, Tome 1994 (1994) no. 4. http://geodesic.mathdoc.fr/item/EJDE_1994__1994_4_a0/