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Nonlocal semilinear second-order differential inclusions in abstract spaces without compactness

Martina Pavlačková, Valentina Taddei (2023)

Archivum Mathematicum

We study the existence of a mild solution to the nonlocal initial value problem for semilinear second-order differential inclusions in abstract spaces. The result is obtained by combining the Kakutani fixed point theorem with the approximation solvability method and the weak topology. This combination enables getting the result without any requirements for compactness of the right-hand side or of the cosine family generated by the linear operator.

Nonuniqueness of implicit lattice Nagumo equation

Petr Stehlík, Jonáš Volek (2019)

Applications of Mathematics

We consider the implicit discretization of Nagumo equation on finite lattices and show that its variational formulation corresponds in various parameter settings to convex, mountain-pass or saddle-point geometries. Consequently, we are able to derive conditions under which the implicit discretization yields multiple solutions. Interestingly, for certain parameters we show nonuniqueness for arbitrarily small discretization steps. Finally, we provide a simple example showing that the nonuniqueness...

Nonuniqueness results for ordinary differential equations

Josef Kalas (1998)

Czechoslovak Mathematical Journal

In the present paper we give general nonuniqueness results which cover most of the known nonuniqueness criteria. In particular, we obtain a generalization of the nonuniqueness theorem of Chr. Nowak, of Samimi’s nonuniqueness theorem and of Stettner’s nonuniqueness criterion.

Note on a discretization of a linear fractional differential equation

Jan Čermák, Tomáš Kisela (2010)

Mathematica Bohemica

The paper discusses basics of calculus of backward fractional differences and sums. We state their definitions, basic properties and consider a special two-term linear fractional difference equation. We construct a family of functions to obtain its solution.

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