Multiple solutions for singularly perturbed semilinear elliptic equations in bounded domains
Ishiwata, Michinori
Abstr. Appl. Anal., Tome 2005 (2005) no. 2, p. 185-205 / Harvested from Project Euclid
We are concerned with the multiplicity of solutions of the following singularly perturbed semilinear elliptic equations in bounded domains $\Omega$:$-\varepsilon^2\Delta u+a(\cdot) u = u|u|^{p-2}$ in $\Omega$ , $u > 0$ in $\Omega$ , $u = 0$ on $\partial\Omega$ . The main purpose of this paper is to discuss the relationship between the multiplicity of solutions and the profile of $a(\cdot)$ from the variational point of view. It is shown that if $a$ has a “peak” in $\Omega$ , then (P) has at least three solutions for sufficiently small $\varepsilon$ .
Publié le : 2005-04-28
Classification: 
@article{1116340208,
     author = {Ishiwata, Michinori},
     title = {Multiple solutions for singularly perturbed
 semilinear elliptic equations in bounded domains},
     journal = {Abstr. Appl. Anal.},
     volume = {2005},
     number = {2},
     year = {2005},
     pages = { 185-205},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1116340208}
}
Ishiwata, Michinori. Multiple solutions for singularly perturbed
 semilinear elliptic equations in bounded domains. Abstr. Appl. Anal., Tome 2005 (2005) no. 2, pp.  185-205. http://gdmltest.u-ga.fr/item/1116340208/