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On the Multiplicity of the Solutions of the Equation −Δu=λ·f(u)

✍ Scribed by Jean Saint Raymond

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
179 KB
Volume
180
Category
Article
ISSN
0022-0396

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✦ Synopsis

Let W be a bounded open subset of R n . We discuss conditions on the continuous function f: R Q R ensuring that the problem -Du=l • f(u) admits unboundedly many weak solutions in H 1 0 (W) for any positive real l.

📜 SIMILAR VOLUMES

On solutions of δu=f(u)
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Existence of multiple positive solutions for −Δu−μ(u/∣x∣2)=u2*−1+σf(x)
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## Abstract In this paper, we consider the semilinear elliptic problem where Ω⊂ℝ^N^ (__N__⩾3) is a bounded smooth domain such that 0∈Ω, σ>0 is a real parameter, $$\mu < \overline{\mu } = (N - 2)^{2} /4$$ and __f__(__x__) is some given function in L^∞^(Ω) such that __f__(__x__)⩾0, __f__(__x__)≢0 i