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Positive solutions for fractional differential equation at resonance under integral boundary conditions

Wang Youyu, Huang Yue, Li Xianfei

Demonstratio Mathematica

2022

Vol. 55, nr 1

238--253

By using the theory of fixed point index and spectral theory of linear operators, we study the existence of positive solutions for Riemann-Liouville fractional differential equations at resonance. Our approach will provide some new ideas for the study of this kind of problem.

A study of chaos for processes under small perturbations II : rigorous proof of chaos

Oprocha P., Wilczyński P.

Opuscula Mathematica

2010

Vol. 30, no. 1

5-36

In the present paper we prove distributional chaos for the Poincaré map in the perturbed equation [formula]. Heteroclinic and homoclinic connections between two periodic solutions bifurcating from the stationary solution 0 present in the system when N = 0 are also discussed.

Solving equations by topological methods

Górniewicz L.

Opuscula Mathematica

2005

Vol. 25, no. 2

195-225

In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in diffrential equations.