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1995 A value function and applications to translation-invariant semilinear elliptic equations on unbounded domains
Ian Schindler
Differential Integral Equations 8(4): 813-828 (1995).

Abstract

We combine results from nonlinear functional analysis relating nonlinear eigenvalues of the type $ g'(u) = \rho u $ to the derivatives of the critical value function $ \gamma (t) := \sup_{\|u\|^2=t} g(u) $ with concentration compactness techniques to study the Dirichlet boundary value problem on $\Omega$, $$ -\Delta u + u = \lambda f(x,u), \tag 0.1 $$ where $\Omega$ is an unbounded cylindrical domain and the dependence on $x$ in the unbounded direction is periodic. We give sufficient conditions on $f$ to obtain an interval in which the $\lambda$'s for which (0.1) has a weak solution are dense.

Citation

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Ian Schindler. "A value function and applications to translation-invariant semilinear elliptic equations on unbounded domains." Differential Integral Equations 8 (4) 813 - 828, 1995.

Information

Published: 1995
First available in Project Euclid: 20 May 2013

zbMATH: 0820.35106
MathSciNet: MR1306593

Subjects:
Primary: 35J60
Secondary: 35P05

Rights: Copyright © 1995 Khayyam Publishing, Inc.

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Vol.8 • No. 4 • 1995
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