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• W2054061612 abstract "We study the second-order nonlinear differential equation $$u'' + a(t) g(u) = 0$$ , where $$g$$ is a continuously differentiable function of constant sign defined on an open interval $$Isubseteq {mathbb R}$$ and $$a(t)$$ is a sign-changing weight function. We look for solutions $$u(t)$$ of the differential equation such that $$u(t)in I,$$ satisfying the Neumann boundary conditions. Special examples, considered in our model, are the equations with singularity, for $$I = {mathbb R}^+_0$$ and $$g(u) sim - u^{-sigma },$$ as well as the case of exponential nonlinearities, for $$I = {mathbb R}$$ and $$g(u) sim exp (u)$$ . The proofs are obtained by passing to an equivalent equation of the form $$x'' = f(x)(x')^2 + a(t)$$ ." @default.
• W2054061612 created "2016-06-24" @default.
• W2054061612 creator A5026016849 @default.
• W2054061612 creator A5063421765 @default.
• W2054061612 date "2013-11-19" @default.
• W2054061612 modified "2023-10-06" @default.
• W2054061612 title "Second-order ordinary differential equations with indefinite weight: the Neumann boundary value problem" @default.
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• W2054061612 doi "https://doi.org/10.1007/s10231-013-0384-0" @default.
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