Nonlinear Discrete Periodic Boundary Value Problems at Resonance

Nonlinear Discrete Periodic Boundary Value Problems at Resonance

Periodic boundary value problems for controlled nonlinear impulsive evolution equations on Banach spaces

This paper deals with the Periodic boundary value problems for Controlled nonlinear impulsive evolution equations. By using the theory of semigroup and fixed point methods, some conditions ensuring the existence and uniqueness. Finally, two examples are provided to demonstrate the effectiveness of the proposed results.

Discrete Boundary-value Problems

We consider multivariate sequences, deened by a partial linear recurrence equation together with appropriate boundary conditions. The domain of deenition of these sequences is the rst orthant of the integer lattice, restricted in some dimensions to an initial segment of the nonnegative integers. By means of the kernel method we obtain an explicit expression for the generating function of the so...

Resonance and Multiplicity in Periodic Boundary Value Problems with Singularity

The paper deals with the boundary value problem u ′′ + k u = g(u) + e(t), u(0) = u(2 ), u(0) = u(2 ), where k ∈ , g : (0,∞) 7→ is continuous, e ∈ [0, 2 ] and lim x→0+ 1 x g(s) ds = ∞. In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.

Resonance and Multiplicity in Periodic Boundary Value Problems with Singularity

The paper deals with the boundary value problem u ′′ + k u = g(u) + e(t), u(0) = u(2 ), u(0) = u(2 ), where k ∈ , g : (0,∞) 7→ is continuous, e ∈ [0, 2 ] and lim x→0+ 1 x g(s) ds = ∞. In particular, the existence and multiplicity results are obtained by using the method of lower and upper functions which are constructed as solutions of related auxiliary linear problems.