Variational approach to impulsive evolution equations

Variational Approach to Impulsive Differential Equations with Dirichlet Boundary Conditions

We study the existence of n distinct pairs of nontrivial solutions for impulsive differential equations with Dirichlet boundary conditions by using variational methods and critical point theory.

Variational approach to a class of impulsive differential equations

The Variational Approach to Nonlinear Evolution Equations

In this paper, we present a few recent existence results via variational approach for the Cauchy problem dy dt (t) + A(t)y(t) ∋ f(t), y(0) = y0, t ∈ [0, T ], where A(t) : V → V ′ is a nonlinear maximal monotone operator of subgradient type in a dual pair (V, V ′) of reflexive Banach spaces. In this case, the above Cauchy problem reduces to a convex optimization problem via Brezis–Ekeland device...

Nonlinear Impulsive Evolution Equations

We study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive evolution equation u′(t) = Au(t) + f(t, u(t)), 0 < t < T0, t = ti, u(0) = u0, ∆u(ti) = Ii(u(ti)), i = 1, 2, ..., 0 < t1 < t2 < ... < T0, in a Banach space X, where A is the generator of a strongly continuous semigroup, ∆u(ti) = u(t+i ) − u(ti ), and Ii’s are some operators. The impulsive conditions c...

Nonlocal Impulsive Cauchy Problems for Evolution Equations

Of concern is the existence of solutions to nonlocal impulsive Cauchy problems for evolution equations. Combining the techniques of operator semigroups, approximate solutions, noncompact measures and the fixed point theory, new existence theorems are obtained, which generalize and improve some previous results since neither the Lipschitz continuity nor compactness assumption on the impulsive fu...