Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics

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Throughout this paper we assume f satisfies the following hypotheses: (f1) f (0) = 0 and f ′ (0) < λ1, (f2) f ′ (∞) ∈ (λk,λk+1), (f3) There is a constant γ such that f ′ (t) ≤ γ < λk+1 <strong>for</strong> every t ∈ R. Under these conditions that we are assuming on f , J ∈ C 2 . MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 6➲ ▲ ▲ ➲ ❏ ✘
Throughout this paper we assume f satisfies the following hypotheses: (f1) f (0) = 0 and f ′ (0) < λ1, (f2) f ′ (∞) ∈ (λk,λk+1), (f3) There is a constant γ such that f ′ (t) ≤ γ < λk+1 <strong>for</strong> every t ∈ R. Under these conditions that we are assuming on f , J ∈ C 2 . We recall that if u is a critical point of J and there exists a maximal integer q such that D 2 J(u) is negative definite on some q-dimensional subspace then the Morse index m(u,J) of u is q. MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 7➲ ▲ ▲ ➲ ❏ ✘
Page 1 and 2: MULTIPLE SOLUTIONS FOR A NONLINEAR
Page 3 and 4: In this lecture we study the nonlin
Page 5: Let λ1,λ2,λ3,... be the sequence
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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