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For 1 eR, consider the boundary value dy d'y +2x x +Ay = 0, xe[1,2]| -(P.) problem dx y(1) = y(2) = 0 Which of the following statements is true? (a) There exists a 2, eR such that (P) has a non-trivial solution for any 1 > A. (b) {2 eR:(P,) has a non-trivial solution} is a dense subset of R (c) For any continuous function f :[1, 2]→ R with f(x)# 0 for some x e (1, 2], there exists a solution u of (P,) for some 1 eR such that fu + 0

For 1 eR, consider the boundary value dy d'y +2x x +Ay = 0, xe[1,2]| -(P.) problem dx y(1) = y(2) = 0 Which of the following statements is true? (a) There exists a 2, eR such that (P) has a non-trivial solution for any 1 > A. (b) {2 eR:(P,) has a non-trivial solution} is a dense subset of R (c) For any continuous function f :[1, 2]→ R with f(x)# 0 for some x e (1, 2], there exists a solution u of (P,) for some 1 eR such that fu + 0

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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For leR, consider the boundary value d'y dy + ly = 0, XE[1,2]| +2x- problem dx dx -(P.) y(1) = y(2) = 0 Which of the following statements is true? (a) There exists a 2, eR such that (P,)has a non-trivial solution for any 1 > A (b) {1 eR: (P) has a non-trivial solution} is a dense subset of R (c) For any continuous function f:[1, 2]→ R with f(x) +0 for some xE [1, 2] , there exists a solution u of (P,) for some 1 eR such that fu +0 (d) There exists a 1 e R such that (P) has two linearly independent solutions
Transcribed Image Text:For leR, consider the boundary value d'y dy + ly = 0, XE[1,2]| +2x- problem dx dx -(P.) y(1) = y(2) = 0 Which of the following statements is true? (a) There exists a 2, eR such that (P,)has a non-trivial solution for any 1 > A (b) {1 eR: (P) has a non-trivial solution} is a dense subset of R (c) For any continuous function f:[1, 2]→ R with f(x) +0 for some xE [1, 2] , there exists a solution u of (P,) for some 1 eR such that fu +0 (d) There exists a 1 e R such that (P) has two linearly independent solutions
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