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Existence of solution to boundary value problem for impulsive differential equations. (English) Zbl 1207.34034
The authors deal with the homogeneous Dirichlet problem $$\aligned &-(|u'(t)|^{p-2}u'(t))' = f(t,u(t),u'(t)), \\ &\Delta u'(t_i) = I_i(u(t_i)), \quad i = 1,2,\dots,\ell,\\ &u(0) = u(T) = 0, \endaligned$$ where $p \geq 2$, $0 < t_1 < \dots < t_\ell < T$, $\Delta u'(t_i) = (|u'|^{p-2}u')(t_i^+) - (|u'|^{p-2}u')(t_i^-)$. The existence of a nontrivial solution is obtained using variational and iterative methods.

34B37Boundary value problems for ODE with impulses
58E30Variational principles on infinite-dimensional spaces
Full Text: DOI
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