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On the existence of sign changing solutions for semilinear Dirichlet problems, Topol. Methods Nonlinear Anal. 7
, 1996
"... We consider the semilinear Dirichlet problem (D) −∆u = f(u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R N is a bounded domain with Lipschitz boundary and f: R → R is of class C 1 with f(0) = 0. Thus u0 ≡ 0 is a trivial solution of (D) and we ..."
Abstract

Cited by 18 (4 self)
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We consider the semilinear Dirichlet problem (D) −∆u = f(u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R N is a bounded domain with Lipschitz boundary and f: R → R is of class C 1 with f(0) = 0. Thus u0 ≡ 0 is a trivial solution of (D) and we
MORSE THEORY OF CAUSAL GEODESICS IN A STATIONARY SPACETIME VIA MORSE THEORY OF GEODESICS OF A FINSLER METRIC
, 903
"... Abstract. We show that the index of a lightlike geodesic in a conformally standard stationary spacetime (M0 × R, g) is equal to the index of its spatial projection as a geodesic of a Finsler metric F on M0 associated to (M0 ×R, g). Moreover we obtain the Morse relations of lightlike geodesics connec ..."
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Cited by 1 (1 self)
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Abstract. We show that the index of a lightlike geodesic in a conformally standard stationary spacetime (M0 × R, g) is equal to the index of its spatial projection as a geodesic of a Finsler metric F on M0 associated to (M0 ×R, g). Moreover we obtain the Morse relations of lightlike geodesics connecting a point p to a curve γ(s) = (q0, s) by using Morse theory on the Finsler manifold (M0, F). To this end, we prove a splitting lemma for the energy functional of a Finsler metric. Finally, we show that the reduction to Morse theory of a Finsler manifold can be done also for timelike geodesics. 1.