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1

Spectrum of discrete 2n-th order difference operator with periodic boundary conditions and its applications

El Amrouss Abdelrachid, Hammouti Omar

Opuscula Mathematica

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2021

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Vol. 41, no. 4

489--507

EN

Let n ∈ N*, and N ≥ n be an integer. We study the spectrum of discrete linear 2n-th order eigenvalue problems [formula] where λ is a parameter. As an application of this spectrum result, we show the existence of a solution of discrete nonlinear 2n-th order problems by applying the variational methods and critical point theory.

2

Multiplicity results for perturbed fourth-order Kirchhoff-type problems

Tavani M. R. H., Afrouzi G. A., Heidarkhani S.

Opuscula Mathematica

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2017

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Vol. 37, no. 5

755--772

EN

In this paper, we investigate the existence of three generalized solutions for fourth-order Kirchhoff-type problems with a perturbed nonlinear term depending on two real parameters. Our approach is based on variational methods.

3

Existence of three solutions for impulsive nonlinear fractional boundary value problems

Heidarkhani S., Ferrara M., Caristi G., Salari A.

Opuscula Mathematica

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2017

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Vol. 37, no. 2

281--301

EN

In this work we present new criteria on the existence of three solutions for a class of impulsive nonlinear fractional boundary-value problems depending on two parameters. We use variational methods for smooth functionals defined on reflexive Banach spaces in order to achieve our results.

4

Multiplicity results for an impulsive boundary value problem of p(t)-Kirchhoff type via critical point theory

Mokhtari A., Moussaoui T., O'Regan D.

Opuscula Mathematica

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2016

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Vol. 36, no. 5

631--649

EN

In this paper we obtain existence results of k distinct pairs nontrivial solutions for an impulsive boundary value problem of p(t)-Kirchhoff type under certain conditions on the parameter λ.

5

Existence of solutions for higher order BVP with parameters via critical point theory

Jurkiewicz M., Przeradzki B.

Demonstratio Mathematica

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2015

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Vol. 48, nr 1

53--61

EN

This paper is concerned with the existence of at least one solution of the nonlinear 2k-th order BVP. We use the Mountain Pass Lemma to get an existence result for the problem, whose linear part depends on several parameters.

6

Existence of three solutions for perturbed nonlinear difference equations

Heidarkhani S., Moghadam M. K.

Opuscula Mathematica

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2014

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Vol. 34, no. 4

747--761

EN

Using critical point theory, we study the existence of at least three solutions for perturbed nonlinear difference equations with discrete boundary-value condition depending on two positive parameters.

7

Multiple solutions for systems of multi-point boundary value problems

Graef J. R., Heidarkhani S., Kong L.

Opuscula Mathematica

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2013

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Vol. 33, no. 2

293--306

EN

In this paper, we establish the existence of at least three solutions of the multi-point boundary value system [formula]. The approaches used are based on variational methods and critical point theory.

8

Periodic solutions for noncoercive superquadratic Hamiltonian systems

Timoumi M.

Demonstratio Mathematica

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2007

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Vol. 40, nr 2

331-346

EN

In this note, we study the existence of periodic solutions for the noncoer- cive Hamiltonian system J ˙ x - u*A(t)u(x) + u*G'(t, u(x)) = 0, where the function G satisfies a new superquadratic condition which includes the case G(t, y) = |y|2(ln(1+|y|p))q, p, q > 1. By using a linking theorem, we obtain some new results.

9

Hemivariational inequalities governed by the p-Laplacian - Neumann problem

Naniewicz Z.

Control and Cybernetics

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2007

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Vol. 36, no 3

727-754

EN

A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition. The existence of solutions for problems with Neumann boundary conditions is established by making use of Chang's version of the critical point theory for nonsmooth locally Lipschitz functionals, combined with the Galerkin method. The approach is based on the recession technique introduced previously by the author.

10

Hemivariational inequalities governed by the p-Laplacian -Dirichlet problem

Naniewicz Z.

Control and Cybernetics

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2004

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Vol. 33, no 2

181-210

EN

A hemivariational inequality involving p-Laplacian is studied under the hypothesis that the nonlinear part fulfills the unilateral growth condition (Naniewicz, 1994). The existence of solutions for problems with Dirichlet boundary conditions is established by making use of Chang's version of the critical point theory for non-smooth locally Lipschitz functionals (Chang, 1981), combined with the Galerkin method. A class of problems with nonlinear potentials fulfilling the classical growth hypothesis without Ainbrosetti-Rabinowitz type assumption is discussed. The approach is based on the recession technique introduced in Naniewicz (2003).

11

On noncoercive elliptic problems with discontinuities

Halidias N.

Journal of Applied Analysis

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2003

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Vol. 9, nr 2

211-223

EN

In this paper using the critical point theory of Chang [4] for locally Lipschitz functionals we prove an existence theorem for non-coercive Neumann problems with discontinuous nonlinearities. We use the mountain-pass theorem to obtain a nontrivial solution.

12

A topological approach to hemivariational inequalities with unilateral growth condition

Motreanu D., Naniewicz Z.

Journal of Applied Analysis

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2001

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Vol. 7, nr 1

23-41

EN

The present paper is devoted to the study of the existence solution problem for a hemivariational inequality on vector-valued function space in the case when the nonlinear nonconvex part satisfies the unilateral growth condition. The critical point theory combined with the Galerkin approximation method have been used to establish the result.