Abstract
We consider the nonlinear Emden–Fowler equation
, where n ∈ ℕ, n ≥ 2, k ∈ ℝ, k > 1, and the function p(t, ξ1,…, ξn) is jointly continuous in all the variables, satisfies the Lipschitz condition with respect to the variables ξ1,…, ξn, and obeys the inequalities m ≤ p(t, ξ1,…, ξn) ≤ M with some positive constants M and m. For this equation, we prove the existence of solutions that are defined on an arbitrary given interval or half-interval and have a prescribed number of zeros.
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Original Russian Text © V.V. Rogachev, 2018, published in Differentsial’nye Uravneniya, 2018, Vol. 54, No. 12, pp. 1638–1644.
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Rogachev, V.V. Existence of Solutions with a Given Number of Zeros to a Higher-Order Regular Nonlinear Emden–Fowler Equation. Diff Equat 54, 1595–1601 (2018). https://doi.org/10.1134/S0012266118120066
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DOI: https://doi.org/10.1134/S0012266118120066