Integration and decompositions of weak∗^*-integrable multifunctions

summary:Conditions guaranteeing Pettis integrability of a Gelfand integrable multifunction and a decomposition theorem for the Henstock-Kurzweil-Gelfand integrable multifunctions are presented

On unbounded solutions for differential equations with mean curvature operator

summary:We present necessary and sufficient conditions for the existence of unbounded increasing solutions to ordinary differential equations with mean curvature operator. The results illustrate the asymptotic proximity of such solutions with those of an auxiliary linear equation on the threshold of oscillation. A new oscillation criterion for equations with mean curvature operator, extending Leighton criterion for linear Sturm-Liouville equation, is also derived

On the behaviour of the solutions of a kk-order cyclic-type system of max difference equations

summary:We investigate the behaviour of the solutions of a $k$-dimensional cyclic system of difference equations with maximum. More precisely, we study the existence and the number of the equilibria in the case when $k$ is an odd or an even positive integer, but also for the various values of the exponents of the terms of the difference equations of this system. In addition, we find invariant intervals for our system and we invistegate the convergence of the solutions to the unique positive equilibrium. Finally, we study the asymptotic behavior of the positive solutions of the system in the case, where $k=2$ and $k=4$

Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay

summary:We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism considered provokes an exponential decay of the solution for the case of equal speed of wave propagation. In the case of lack of exponential stability, we show that the solution decays polynomially

Stieltjes differential problems with general boundary value conditions. Existence and bounds of solutions

summary:We are concerned with first order set-valued problems with very general boundary value conditions \begin{cases} u'_g(t)\in F(t,u(t)),\quad \mu _g \text {-a.e.} \t\in [0,T] , \\ L(u(0),\u(T))=0 \end{cases} involving the Stieltjes derivative with respect to a left-continuous nondecreasing function $g\colon [0,T]\to \mathbb {R}$, a Carathéodory multifunction $F\colon [0,T]\times \mathbb {R}\to \mathcal {P}(\mathbb {R})$ and a continuous $L\colon \mathbb {R}^2\to \mathbb {R}$. Using appropriate notions of lower and upper solutions, we prove the existence of solutions via a fixed point result for condensing mappings. In the periodic single-valued case, combining an existence theory for the linear case with a recent result involving lower and upper solutions (which can be seen as a consequence of our existence theorem mentioned before), we get not only the existence of solutions, but also lower and upper bounds, respectively, by imposing an estimation for the right-hand side

Positive periodic solutions to super-linear second-order ODEs

summary:We study the existence and uniqueness of a positive solution to the problem $$u''=p(t)u+q(t,u)u+f(t);\quad u(0)=u(\omega ),\ u'(0)=u'(\omega )$$ with a super-linear nonlinearity and a nontrivial forcing term $f$. To prove our main results, we combine maximum and anti-maximum principles together with the lower/upper functions method. We also show a possible physical motivation for the study of such a kind of periodic problems and we compare the results obtained with the facts well known for the corresponding autonomous case

The Picard-Lindelöf Theorem and continuation of solutions for measure differential equations

summary:We obtain, by means of Banach's Fixed Point Theorem, convergence for the Picard iterations associated to a general nonlinear system of measure differential equations. We study the existence of left-continuous solutions defined on maximal intervals and we establish some properties of these maximal solutions

Two-step Ulm-Chebyshev-like method for inverse singular value problems with multiple singular values

summary:We study the convergence of two-step Ulm-Chebyshev-like method for solving the inverse singular value problems. We focus on the case when the given singular values are positive and multiple. This work extends the result of W. Ma (2022). We show that the new method is cubically convergent. Moreover, numerical experiments are given in the last section, which show that the proposed method is practical and efficient

The origin and developments of Kurzweil's generalized Riemann integral

summary:The paper describes to origin and motivation of Kurzweil in introducing a Riemann-type definition for generalized Perron integrals and his further contributions to the topics

Efficiency analysis of the rule-based defuzzification approach to fuzzy inference system for regression problems

summary:A fuzzy inference system (FIS) is an effective prediction method based on fuzzy logic. The performance of this model may vary depending on the defuzzification process. In the Mamdani-type FIS model, the defuzzification process is applied to the fuzzy output of the system only once at the last stage. In the FIS with rule-based defuzzification (FIS-RBD) model, the defuzzification process is applied to the fuzzy consequent part of each rule and the overall result of the system is calculated as the weighted average of the separately defuzzified results of the rules. Note that, the original shapes of the combined rule results are lost in the aggregated fuzzy result of the classical Mamdani-type system and the effect of each rule on the system result decreases when aggregated. However, rule results can affect the overall result more significantly in the FIS-RBD approach. In this study, a comparative analysis was made on the effectiveness of the classical Mamdani-type FIS and FIS-RBD models for regression problems. Five datasets from different domains and various defuzzification methods were used in comparisons. In the results obtained, it was observed that the The FIS-RBD model gave better results than the classical Mamdani-type FIS model. To carry out calculation experiments, a new Python package called Fuzlab was developed by modifying the existing Python library called FuzzyLab. In addition to creating the FIS-RBD model, the developed package also allows the use of the Weighted Average Based on Levels (WABL) defuzzification method in fuzzy logic-based calculations