Stepan Tersian

Existence of solutions to boundary value problem for impulsive fractional differential equations

In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fractional order differential equations. The notions of classical and weak solutions are introduced. Then, existence results of at least one and three solutions are proved.

Multiple solutions to boundary value problem for impulsive fractional differential equations

We study the multiplicity of solutions for fractional differential equations subject to boundary value conditions and impulses. After introducing the notions of classical and weak solutions, we prove the existence of at least three solutions to the impulsive problem considered.

An introduction to minimax theorems and their applications to differential equations

Preface. 1. Minimization and Mountain-Pass Theorems. 2. Saddle-Point and Linking Theorems. 3. Applications to Elliptic Problems in Bounded Domains. 4. Periodic Solutions for Some Second-Order Differential Equations. 5. Dual Variational Method and Applications. 6. Minimax Theorems for Locally Lipschitz Functionals and Applications. 7. Homoclinic Solutions of Differential Equations. Notations. Index.

On the solvability of a boundary value problem for a fourth-order ordinary differential equation

We study the existence and multiplicity of nontrivial periodi cs olutions for a semilinear fourth-order ordinary differential equation arising in the study of spatial patterns for bistable systems. Variational tools such as the Brezis–Nirenberg theorem and Clark theorem are used in the proofs of the main results.

Multiplicity of solutions of a two point boundary value problem for a fourth-order equation

We study the existence of multiple solutions for semi linear fourth-order differential equation describing elastic deflections. The proof of the main result is based on a three critical point theorem.

Spectral estimates for a nonhomogeneous difference problem

We study an eigenvalue problem in the framework of difference equations. We show that there exist two positive constants λ0 and λ1 verifying λ0 ≤ λ1 such that any λ ∈ (0, λ0) is not an eigenvalue of the problem, while any λ ∈ [λ1, ∞) is an eigenvalue of the problem. Some estimates for λ0 and λ1 are also given.

On Homoclinic Solutions of a Semilinear -Laplacian Difference Equation with Periodic Coefficients

We study the existence of homoclinic solutions for semilinear -Laplacian difference equations with periodic coefficients. The proof of the main result is based on Brezis-Nirenbergs Mountain Pass Theorem. Several examples and remarks are given.

Periodic and homoclinic solutions of some semilinear sixth-order differential equations

In this paper we study the existence of periodic solutions of the sixth-order equation uvi+Auiv+Bu″+u−u3=0, where the positive constants A and B satisfy the inequality A2<4B. The boundary value problem (P) is considered with the boundary conditions u(0)=u″(0)=uiv(0)=0,u(L)=u″(L)=uiv(L)=0. Existence of nontrivial solutions for (P) is proved using a minimization theorem and a multiplicity result using Clarks theorem. We study also the homoclinic solutions for the sixth-order equation uvi+Auiv+Bu″−u+a(x)u|u|σ=0, where a is a positive periodic function and σ is a positive constant. The mountain-pass theorem of Brezis–Nirenberg and concentration-compactness arguments are used.

Existence and multiplicity of solutions to boundary value problems for fourth-order impulsive differential equations

In this paper we study the existence and the multiplicity of solutions for an impulsive boundary value problem for fourth-order differential equations. The notions of classical and weak solutions are introduced. Then the existence of at least one and infinitely many nonzero solutions is proved, using the minimization, the mountain-pass, and Clarke’s theorems.MSC: 34B15, 34B37, 58E30.

On the Existence and Multiplicity of Solutions for Dirichlet’s problem for Fractional Differential equations

Abstract In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.