@article {26902,
title = {New competition phenomena in Dirichlet problems},
journal = {Journal de Mathematiques Pures et Appliquees},
volume = {94},
year = {2010},
pages = {555{\textendash}570},
abstract = {We study the multiplicity of nonnegative solutions to the problem, (Pλ) where Ω is a smooth bounded domain in RN, f:[0,$\infty$){\textrightarrow}R oscillates near the origin or at infinity, and p>0, λ∈R. While oscillatory right-hand sides usually produce infinitely many distinct solutions, an additional term involving up may alter the situation radically. Via a direct variational argument we fully describe this phenomenon, showing that the number of distinct non-trivial solutions to problem (Pλ) is strongly influenced by up and depends on λ whenever one of the following two cases holds:
{\textbullet}p⩽1 and f oscillates near the origin;
{\textbullet}p⩾1 and f oscillates at infinity (p may be critical or even supercritical).
The coefficient a∈L$\infty$(Ω) is allowed to change its sign, while its size is relevant only for the threshold value p=1 when the behaviour of f(s)/s plays a crucial role in both cases. Various - and L$\infty$-norm estimates of solutions are also given.},
url = {http://www.sciencedirect.com/science/article/pii/S0021782410000383},
author = {Krist{\'a}ly, Alexandru and Morosanu, Gheorghe}
}