# Publications of Tersian, Stepan

Homoclinic solutions of difference equations with variable exponents

We study the existence of homoclinic solutions for a class of non-homogeneous difference equation with periodic coefficients. Our proofs rely on the critical point theory combined with adequate variational techniques, which are mainly based on the mountain-pass lemma.

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.

Eigenvalue Problems for Anisotropic Discrete Boundary Value Problems

In this paper, we prove the existence of a continuous spectrum for a family of discrete boundary value problems. The main existence results are obtained by using critical point theory. The equations studied in the paper represent a discrete variant of some recent anisotropic variable exponent problems which serve as models in di®erent ¯elds of mathematical physics.