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- W2079380208 abstract "We are interested in the oscillatory behavior of solutions of the Emden–Fowler equation y ″ + a ( x ) | y | γ − 1 y = 0 , γ > 1 , where a ( x ) is a positive continuous function on ( 0 , ∞ ) . In the special case when the coefficient a ( x ) is a power of x , i.e. a ( x ) = x α for some constant α , the value α ∗ = − ( γ + 3 ) / 2 plays a critical role: The equation has both oscillatory and nonoscillatory solutions if α > α ∗ , while all solutions are nonoscillatory if α < α ∗ . When a ( x ) is close to the critical exponent, one of the known results is that if a ( x ) = x − ( γ + 3 ) / 2 log − σ ( x ) , where σ > 0 , then all solutions are nonoscillatory. In this paper, this result is further extended to include a class of coefficients in which the above condition with log ( x ) can be replaced by log log ( x ) , or log log log ( x ) and so on." @default.
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- W2079380208 date "2007-07-01" @default.
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- W2079380208 title "A nonoscillation theorem for superlinear Emden–Fowler equations with near-critical coefficients" @default.
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- W2079380208 doi "https://doi.org/10.1016/j.jde.2007.03.021" @default.
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