Displaying similar documents to “On quadratically integrable solutions of the second order linear equation”

Existence of positive solutions for a class of higher order neutral functional differential equations

Satoshi Tanaka (2001)

Czechoslovak Mathematical Journal

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The higher order neutral functional differential equation d n d t n x ( t ) + h ( t ) x ( τ ( t ) ) + σ f t , x ( g ( t ) ) = 0 ( 1 ) is considered under the following conditions: n 2 , σ = ± 1 , τ ( t ) is strictly increasing in t [ t 0 , ) , τ ( t ) < t for t t 0 , lim t τ ( t ) = , lim t g ( t ) = , and f ( t , u ) is nonnegative on [ t 0 , ) × ( 0 , ) and nondecreasing in u ( 0 , ) . A necessary and sufficient condition is derived for the existence of certain positive solutions of (1).

Eventual disconjugacy of y ( n ) + μ p ( x ) y = 0 for every μ

Uri Elias (2004)

Archivum Mathematicum

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The work characterizes when is the equation y ( n ) + μ p ( x ) y = 0 eventually disconjugate for every value of μ and gives an explicit necessary and sufficient integral criterion for it. For suitable integers q , the eventually disconjugate (and disfocal) equation has 2-dimensional subspaces of solutions y such that y ( i ) > 0 , i = 0 , ... , q - 1 , ( - 1 ) i - q y ( i ) > 0 , i = q , ... , n . We characterize the “smallest” of such solutions and conjecture the shape of the “largest” one. Examples demonstrate that the estimates are sharp.