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Necessary and Sufficient Tauberian Condition for Both Cesàro and Abel Summability
We prove that the Weakly-Vanishing Mean Oscillation ( W-VMO ) property of a sequence or a series is a necessary and sufficient condition under which...
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A Necessary Condition for HK-Integrability of the Fourier Sine Transform Function
The paper is concerned with integrability of the Fourier sine transform function when f ∈ BV 0 (ℝ), where BV 0 (ℝ) is the space of bounded variation...
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A Necessary Condition on a Singular Kernel for the Continuity of an Integral Operator in Hölder Spaces
We prove that a condition of boundedness of the maximal function of a singular integral operator, that is known to be sufficient for the continuity...
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A necessary and sufficient condition of blow-up for a nonlinear equation
We investigate a nonlinear equation with quadratic nonlinearities, including a nonlinear model in Silva and Freire (J. Differ. Equ. 320:371–398,
2022 )... -
A necessary and sufficient condition for the existence of global solutions to reaction-diffusion equations on bounded domains
The purpose of this paper is to give a necessary and sufficient condition for the existence and non-existence of global solutions of the following...
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A sufficient and necessary condition for one dimensional boundary blow-up problem with p-Laplace operator
The existence, uniqueness and asymptotic behavior for one dimensional boundary blow-up problem with p-Laplace operator has been investigated. This...
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A Necessary Condition for Non-Oscillatory and Positivity Preserving Time-Integration Schemes
Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for...
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Sufficient close-to-necessary condition for the existence of homoclinic orbits, and applications
In this paper, we give a general and weak sufficient condition to guaranteeing the existence of infinitely many homoclinic solutions for some classes...
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Necessary and sufficient condition for boundedness of translation operator in de Branges spaces
In the previous work Bellavita (Complex Anal. Oper. Theory 15: 96, 2021) we found some necessary conditions for the boundedness of the translation...
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The convergence rate and necessary-and-sufficient condition for the consistency of isogeometric collocation method
Although the isogeometric collocation (IGA-C) method has been successfully utilized in practical applications due to its simplicity and efficiency,...
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Necessary Condition for the Existence of Unconditional Bases of Reproducing Kernels for Hilbert Spaces of Entire Functions
We consider an abstract radial Hilbert function spaces H stable under division and find a necessary condition for the existence of unconditional...
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Legendre’s Necessary Condition for Fractional Bolza Functionals with Mixed Initial/Final Constraints
The present work was primarily motivated by our findings in the literature of some flaws within the proof of the second-order Legendre necessary...
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Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications
In this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative)...
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First- and Second-Order Necessary Optimality Conditions for a Control Problem Described by Nonlinear Fractional Difference Equations
AbstractThis paper considers an optimal control problem for an object described by a system of nonlinear fractional difference equations. Such...
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A necessary and sufficient condition for sequences to be minimal completely monotonic
In this article, we present a necessary and sufficient condition under which sequences are minimal completely monotonic.
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System without Characteristic Directions with a Nonanalytic Center Condition
AbstractA real autonomous differential system of the fifth degree with a degenerate singular point without characteristic directions is obtained....
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The Case of Symmetric Two-Dimensional Domains: General Outflow Condition
In this chapter, we demonstrate that in a certain class of symmetric two-dimensional domains, Hopf’s lemma remains valid even when the strict outflow...
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Necessary and Sufficient Condition for the Existence of a Classical Solution of the Inhomogeneous Biharmonic Equation
AbstractWe prove that a necessary and sufficient condition for the existence of a classical solution of the inhomogeneous biharmonic equation in a...
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On Tucker-Type Alternative Theorems and Necessary Optimality Conditions for Nonsmooth Multiobjective Optimization
This paper concentrates on necessary conditions for properly efficient solutions in nonsmooth multiobjective optimization problems. We first present...