The solvability results are established for the boundary value problem with a damping term, h is a bounded nonlinearity, µ, λ real parameters. The existence results are based of the knowledge of the Fučík type spectrum for the problem with h ≡ 0.

Abstract. The basic mathematical skills are acquired in elementary school. This research compares basic mathematical knowledge of three groups -elementary school graduates, students from four different specialties (future engineers) with varied levels of higher mathematics and future teachers of mathematics. The study concludes that students from elementary school have better knowledge in comparison with students from university. The possible reason for that is resent acquirement of the study material and examination at finishing elementary school. It is also observed that several students had taken gap years between school and university, but the current educational system in Latvia does not require entrance examinations. Modern engineering education is founded on good basics of mathematics that are acquired in elementary school. The experience shows that acquisition of the course of mathematics at elementary school is the determinant factor for further successful acquisition of the course of higher mathematics.

The solvability results are established for the boundary value problem , where x + = max{x, 0}, x - = max{-x, 0}, h is a bounded nonlinearity. The existence results are based of the knowledge of the spectrum for the problem with h ≡ 0.

Abstract. We study the second order nonlinear boundary value problems with nonlocal integral conditions and construct the Fučík type spectrum for these problems.

Abstract. Boundary value problem of the form x = −µxx(s) ds = 0 is considered, where µ, λ ∈ R and α ∈ [0, 1]. The explicit formulas for the spectrum of this problem are given and the spectra for some α values are constructed. Special attention is paid to the spectrum behavior at the points close to the coordinate origin.