Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics

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Let λ1,λ2,λ3,... be the sequence of eigenvalues of −Δ in Ω with zero <strong>Dirichlet</strong> boundary condition. MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 4➲ ▲ ▲ ➲ ❏ ✘
Let λ1,λ2,λ3,... be the sequence of eigenvalues of −Δ in Ω with zero <strong>Dirichlet</strong> boundary condition. As it is well known, to solve (0.1) is equivalent to find critical points of the functional J : H 1 0 where F(ξ) = � ξ 0 (Ω) → R defined by � � 1 J(u) = 2 |∇u|2 � − F(u) f (s) ds. Ω MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 5➲ dx, (0.2) ▲ ▲ ➲ ❏ ✘
Page 1 and 2: MULTIPLE SOLUTIONS FOR A NONLINEAR
Page 3: In this lecture we study the nonlin
Page 7 and 8: Throughout this paper we assume f s
Page 9 and 10: Theorem A. If f satisfies (f1), (f2
Page 11 and 12: Theorem A. If f satisfies (f1), (f2
Page 13 and 14: REMARK: We prove the existence of u
Page 15 and 16: REMARK: We prove the existence of u
Page 17 and 18: Sketch of the Proof of Theorem A: B
Page 19 and 20: Sketch of the Proof of Theorem A: L
Page 21 and 22: Sketch of the Proof of Theorem A: T
Page 33 and 34: Sketch of the Proof of Theorem A: O
Page 37 and 38: Sketch of the Proof of Theorem A: S
Page 39 and 40: Sketch of the Proof of Theorem A: C
Page 41 and 42: Sketch of the Proof of Theorem A: N
Page 43 and 44: Sketch of the Proof of Theorem A: W
Page 45 and 46: Sketch of the Proof of Theorem A: W
Page 47 and 48: References Solutions of a Nonlinear
Page 49: Fin Copyright c○ 2008 Jorge Cossi

Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics

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