Existence of positive solutions of a singular nonlinear boundary value problem.

Ma, Ruyun; Li, Jiemei

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The existence, uniqueness and regularities of the generalized global solutions and classical global solutions to the equation $u_{t} = - A (t) u_{x^{4}} + B (t) u_{x^{2}} + g {(u)}_{x^{2}} + f {(u)}_{x} + h {(u_{x})}_{x} + G (u)$ with the initial boundary value conditions $u (- ℓ, t) = u (ℓ, t) = 0, u_{x^{2}} (- ℓ, t) = u_{x^{2}} (ℓ, t) = 0, u (x, 0) = ϕ (x),$ or with the initial boundary value conditions $u_{x} (- ℓ, t) = u_{x} (ℓ, t) = 0, u_{x^{3}} (- ℓ, t) = u_{x^{3}} (ℓ, t) = 0, u (x, 0) = ϕ (x),$ are proved. Moreover, the asymptotic behavior of these solutions is considered under some conditions.

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