Multiple Solutions for a Nonlinear Dirichlet Problem via - Mathematics

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Sketch of the Proof of Theorem A: Because of (f1), u1 ≡ 0 is a strict local minimum of J, so dloc(∇J,u1) = 1. MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 16➲ ▲ ▲ ➲ ❏ ✘
Sketch of the Proof of Theorem A: Because of (f1), u1 ≡ 0 is a strict local minimum of J, so dloc(∇J,u1) = 1. The existence of the two signed-solutions u2 > 0 in Ω and u3 < 0 in Ω is proved by using the Mountain Pass Theorem. Moreover, dloc(∇J,u2) = dloc(∇J,u3) = −1, (0.3) MULTIPLE SOLUTIONS FOR A NONLINEAR DIRICHLET PROBLEM VIA MORSE INDEX – 17➲ ▲ ▲ ➲ ❏ ✘
Page 1 and 2: MULTIPLE SOLUTIONS FOR A NONLINEAR
Page 3 and 4: In this lecture we study the nonlin
Page 5 and 6: Let λ1,λ2,λ3,... be the sequence
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: REMARK: We prove the existence of u
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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