Displaying similar documents to “Periodic-Neumann boundary value problem for nonlinear parabolic equations and application to an elliptic equation”

On a nonlinear second order periodic boundaryvalue problem with Carathéodory functions

Wenjie Gao, Junyu Wang (1995)

Annales Polonici Mathematici

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The periodic boundary value problem u''(t) = f(t,u(t),u'(t)) with u(0) = u(2π) and u'(0) = u'(2π) is studied using the generalized method of upper and lower solutions, where f is a Carathéodory function satisfying a Nagumo condition. The existence of solutions is obtained under suitable conditions on f. The results improve and generalize the work of M.-X. Wang et al. [5].

Existence of solutions and monotone iterative method for infinite systems of parabolic differential-functional equations

Stanisław Brzychczy (1999)

Annales Polonici Mathematici

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We consider the Fourier first boundary value problem for an infinite system of weakly coupled nonlinear differential-functional equations. To prove the existence and uniqueness of solution, we apply a monotone iterative method using J. Szarski's results on differential-functional inequalities and a comparison theorem for infinite systems.