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Successive iterative method for higher-order fractional differential equations involving Stieltjes integral boundary conditions

Jankowski T.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2016

Vol. 20, No 1

99--108

In this paper, the existence of positive solutions to fractional differential equations with delayed arguments and Stieltjes integral boundary conditions is discussed. The convergence of successive iterative method of solving such problems is investigated. This allows us to improve some recent works. Some numerical examples illustrate the results.

Multiple solutions to third-order differential equations with derivative dependence and deviating arguments

Jankowski T.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2016

Vol. 20, No 1

85--98

In this paper, we give some new results for multiplicity of positive (nonnegative) solutions for third-order differential equations with derivative dependence, deviating arguments and Stieltjes integral boundary conditions. We discuss our problem with advanced argument α and arbitrary β ∈ C([0,1],[0,1]), see problem (2). It means that argument β can change the character on [0,1], so β can be delayed in some set J¯⊂ [0,1] and advanced in [0,1] \ J¯. Four examples illustrate the main results

Oscillation properties of a class of neutral differential equations with positive and negative coefficients

Tripathy A. K.

Fasciculi Mathematici

2010

Nr 45

133-155

In this paper, oscillatory and asymptotic property of solutions of a class of nonlinear neutral delay differential equations of the form (E) ...[wzór] and ...[wzór] are studied under the assumptions ...[wzór] and ...[wzór] for various ranges of p(t). Sufficient conditions are obtained for existence of bounded positive solutions of (E).