Existence of solution to boundary value problem for impulsive differential equations.(English)Zbl 1207.34034

The authors deal with the homogeneous Dirichlet problem
\begin{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, \end{aligned}
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.

MSC:

 34B37 Boundary value problems with impulses for ordinary differential equations 58E30 Variational principles in infinite-dimensional spaces
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References:

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