Study of an impulsive second-order mixed boundary value problem with a parameter using variational methods.
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Date
2024-06
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Abstract
In this memoiry, we have studied an impulsive second-order boundary value problem on the
bounded domain [0, T], as well as the theory of critical points, the mountain pass lemma and
the saddle point theorem. Our goal in this study was to apply the critical point theory, neck
lemma and saddle point theorem to verify the existence and multiplicity of solutions to the
following impulsive second-order boundary value problem :
−u
00(t) = λu(t) + f(t, u(t)), t 6= ti
, t ∈ [0, T],
−∆u
0
(ti) = Ii(u(ti)), i = 1, 2, ..., l,
u
0
(0) = 0, u(T) = 0.
Description
Keywords
Critical point, Variational method, Existence of solutions, Second order, Impulsive differential equation, Mountain pass lemma, Saddle point theorem, Palais-Smale Condition, Derivative dependence, Energy functional