# Vol 21, No 6 (2015)

**Year:**2015**Articles:**24**URL:**https://journals.ssau.ru/est/issue/view/218

## Статьи

### ON OSCILLATION OF SOLUTIONS TO QUASI-LINEAR EMDEN – FOWLER TYPE HIGHER-ORDER DIFFERENTIAL EQUATIONS

#### Abstract

Existence and behavior of oscillatory solutions to nonlinear equations with regular and singular power nonlinearity are investigated. In particular, the existence of oscillatory solutions is proved for the equation y(n) + P(x; y; y ′ ; : : : ; y(n−1))|y|k sign y = 0; n > 2; k ∈ R; k > 1; P ̸= 0; P ∈ C(Rn+1): A criterion is formulated for oscillation of all solutions to the quasilinear even-order differential equation y(n) + nΣ−1 i=0 aj(x) y(i) + p(x) |y|ksigny = 0; p ∈ C(R); aj ∈ C(R); j = 0; : : : ; n − 1; k > 1; n = 2m; m ∈ N; which generalizes the well-known Atkinson’s and Kiguradze’s criteria. The existence of quasi-periodic solutions is proved both for regular (k > 1) and singular (0 < k < 1) nonlinear equations y(n) + p0 |y|ksigny = 0; n > 2; k ∈ R; k > 0; k ̸= 1; p0 ∈ R; with (−1)np0 > 0: A result on the existence of periodic oscillatory solutions is formulated for this equation with n = 4; k > 0; k ̸= 1; p0 < 0:

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):12-22

### ESTIMATES OF POSITIVE NONTRIVIAL SOLUTIONS OF A DIFFERENTIAL EQUATION WITH POWER NONLINEARITY

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):23-26

### Integral representations of solutionsof Riquier for polyharmonic equations in n-dimensional ball

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):27-39

### ON REPRESENTATION OF MODULAR FORMS AS HOMOGENEOUS POLYNOMIALS

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):40-49

### Asymptotic classiﬁcation of solutionsto the second-order Emden - Fowler type diﬀerential equation with negativepotential

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):50-56

### ON A MINIMIZATION PROBLEM FOR A FUNCTIONAL GENERATED BY THE STURM – LIOUVILLE PROBLEM WITH INTEGRAL CONDITION ON THE POTENTIAL

#### Abstract

In this article we consider the minimization problem of the functional generated by a Sturm — Liouville problem with Dirichlet boundary conditions and with an integral condition on the potential. Estimation of the infimum of functional in some class of functions y and Q(x) is

reduced to estimation of a nonlinear functional non depending on the potential Q(x). This leads to related parameterized nonlinear boundary value problem. Upper and lower estimates are obtained for different values of parameter.

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):57-61

### Inverse problems for the heat equation

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):62-75

### Finding of a numerical solution tothe Cauchy - Dirichlet problem for Boussinesq - Lo`ve equation using ﬁnitediﬀerences method

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):76-81

### One generalization of Marchaud inequality onsignsensitive weights

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):82-88

### On the maximum principle for a class of nonlinear parabolicequations

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):89-92

### Numerical investigation of thegeneralized Hoﬀ model

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):93-97

### GERSTEN COMPLEX FOR SHEAVES WITH TRANSFERS FOR NOETHERIAN SCHEMES

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):98-101

### UNCERTAINTY PRINCIPLES FOR GROUPS AND RECONSTRUCTION OF SIGNALS

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):102-109

### ON SOLUTIONS OF TRAVELING WAVE TYPE FOR A NONLINEAR PARABOLIC EQUATION

#### Abstract

We consider the Kolmogorov — Petrovsky — Piskunov equation which is

a quasilinear parabolic equation of second order appearing in the flame propagation

theory and in modeling of certain biological processes. An analytical

construction of self-similar solutions of traveling wave kind is presented for the

special case when the nonlinear term of the equation is the product of the

argument and a linear function of a positive power of the argument. The approach

to the construction of solutions is based on the study of singular points

of analytic continuation of the solution to the complex domain and on applying

the Fuchs — Kovalevskaya — Painlev´e test. The resulting representation of the

solution allows an efficient numerical implementation.

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):110-116

### ON THE EXISTENCE OF SOLUTIONS WITH PRESCRIBED NUMBER OF ZEROS TO REGULAR NONLINEAR EMDEN - FOWLER TYPE THIRD-ORDER EQUATION WITH VARIABLE COEFFICIENT

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):117-123

### ON THE UPPER ESTIMATES FOR THE FIRST EIGENVALUE OF A STURM - LIOUVILLE PROBLEM WITH A WEIGHTED INTEGRAL CONDITION

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):124-129

### ON ASYMPTOTIC PROPERTIES OF SOLUTIONS, DEFINED ON THE HALF OF AXIS OF ONE SEMILINEAR ODE

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):130-134

### ON THE ASYMPTOTIC BEHAVIOR OF EIGENVALUES OF THE BOUNDARY VALUE PROBLEM WITH A PARAMETER

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):135-140

### ABOUT NUMERICAL MODELLING OF THOMSON SELF-OSCILLATORY SYSTEMS

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):141-150

### DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH THERMAL FIELD FOR ENTANGLED INITIAL ATOMIC STATES

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):151-160

### MONTE-CARLO CALCULATIONS OF PHASE TRANSITION TEMPERATURE IN THE ISING MODEL WITH LONG RANGE INTERACTIONS

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):161-170

### CONSTRUCTION OF SYSTEMS OF PROTECTION FROM UNAUTHORIZED ACCESS FOR INFORMATION SYSTEMS TAMPER LOCATED IN THE INDUSTRIAL USE

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):171-177

### FEATURES OF FUNCTIONAL PROGRAMMING OF INTERACTIVE GRAPHICAL APPLICATIONS

#### Abstract

**Vestnik of Samara University. Natural Science Series**. 2015;21(6):178-189