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Multiplicity of solutions for nonlinear second order impulsive differential equations with linear derivative dependence via variational methods. (English) Zbl 1251.34046
The authors consider the impulsive boundary value problem $$ \aligned &-(p(t)u'(t))' + r(t)u'(t) + q(t)u(t) = f(t,u(t)) \, \text{for} \,\, \text{a.e.}\,\, t \in [0,T],\ t \ne t_j,\\ &-\Delta(p(t_j)u'(t_j)) = I_j(u(t_j)), \quad j = 1,\dots,n,\\ & u(0) = 0, a_1u(1) + u'(1) = 0, \endaligned $$ where $0 < t_1 < \dots < t_n < 1$, $f \in C[[0,1]\times{\Bbb R}, {\Bbb R}]$, $p \in C^1[0,1]$, $q \in C[0,1]$. There are obtained multiplicity existence results for this type of BVP. As a main tool, variational methods are used.

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