Existence and multiplicity of solutions for an impulsive second-order boundary value problem with Dirichlet boundary conditions via 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 theorem
and the saddle point theorem. Our goal in this study was to apply the critical point theory,
Mountain pass theorem, saddle point theorem and Symmetric Mountain Pass 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 ∈ [0, T],
∆u
0
(tj ) = Ij (u(tj )), j = 1, 2, ..., p,
u(0) = u(T) = 0,
Description
Keywords
Variational method, Critical point, Existence of solutions, Second order, Impulsive differential equation, Mountain pass theorem, Palace-Smale Condition, Saddle point theorem, Symmetric Mountain Pass Theorem