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Currently displaying 1 – 5 of 5

Order by Relevance | Title | Year of publication

A note about a priori estimates for indefinite problems in unbounded domains.

Jacques Giacomoni — 2003

RACSAM

Some results about blow-up and global existence to a semilinear degenerate heat equation.

Jacques Giacomoni — 1998

Revista Matemática Complutense

Positive solutions for elliptic problems with critical indefinite nonlinearity in bounded domains.

Giacomoni, Jacques; Prajapat, Jyotshana V.; Ramaswamy, Mythily — 2007

Electronic Journal of Differential Equations (EJDE) [electronic only]

A variational approach to bifurcation into spectral gaps

Jacques Giacomoni; Louis Jeanjean — 1999

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Sobolev versus Hölder local minimizers and existence of multiple solutions for a singular quasilinear equation

Jacques Giacomoni; Ian Schindler; Peter Takáč — 2007

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We investigate the following quasilinear and singular problem, $t o 2.7 c m \{\begin{matrix} - Δ_{p} u = \frac{λ}{u^{δ}} + u^{q} & in Ω; \\ {u |}_{\partial Ω} = 0, u > 0 & in Ω, \end{matrix} t o 2.7 c m (P)$ where $Ω$ is an open bounded domain with smooth boundary, $1 < p < \infty$ , $p - 1 < q \leq p^{*} - 1$ , $λ > 0$ , and $0 < δ < 1$ . As usual, $p^{*} = \frac{N p}{N - p}$ if $1 < p < N$ , $p^{*} \in (p, \infty)$ is arbitrarily large if $p = N$ , and $p^{*} = \infty$ if $p > N$ . We employ variational methods in order to show the existence of at least two distinct (positive) solutions of problem (P) in $W_{0}^{1, p} (Ω)$ . While following an approach due to Ambrosetti-Brezis-Cerami, we need to prove two new results of separate interest: a strong comparison principle and a...

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