[PDF] Top 20 An Overview of the Lower and Upper Solutions Method with Nonlinear Boundary Value Conditions

... In the classical books of Bernfeld and Lakshmikantham 6 and Ladde et al. 7 the classical theory of the method of lower and upper solutions and the monotone iterative technique are given. This ... See full document

... interface boundary value problem ...a lower and upper solutions lemma which is an extension of classical theory of lower and upper solutions (see [], for ...the ... See full document

... The method of upper and lower solutions and the Schauder fixed point theorem are used to investigate the existence and uniqueness of a positive solution to a singular boundary ... See full document

... the method of upper and lower solu- tions has been used to study the existence of extremal solutions of periodic boundary value problems for second-order impulsive equations; ... See full document

... of upper and lower solutions is also a powerful tool in studying boundary value ...two-point boundary value problem, there already are lots of interesting works by ... See full document

... new method of lower and upper solutions for a general boundary value problem of fractional differential equations with p-Laplacian ...positive solutions for the equations ... See full document

... It is called periodic boundary value problems(PBVP) for the system of nonlinear Riemann-Liouville fractional differential equations. Assume that J = [0, T ] ⊂ R is a compact inter- val and f i (t, u ... See full document

... positive solutions for a class of multi-order systems of fractional differential equations with nonlocal ...and upper and lower solutions ... See full document

... finding upper and lower solutions is very ...of lower and upper solutions has been solved very rarely (see, ...present conditions ensuring the existence of nonconstant ... See full document

... Positive Solutions for Eigenvalue Problems of Fractional Differential Equation with Generalized ...The Method of Lower and Upper Solutions for ... See full document

... of upper and lower solution technique and the fixed point theory, for instance, Krasnoselskii fixed point theorem, the fixed point index of a completely continuous operator with respect to a cone in a ... See full document

... homogeneous boundary value problem corresponding to (1)-(2) is constructed and certain lemmas are ...sufficient conditions for the existence of a positive solution of fractional order boundary ... See full document

... global solutions, bounds for blow-up time, blow-up rate, blow-up sets and asymptotic behavior for this type of equations were investigated by many ...initial boundary value problem for the above ... See full document

... of solutions to the fully fourth- order nonlinear boundary value problem ...fourth-order nonlinear BVPs with the boundary condition in BVP ...other boundary ... See full document

... of boundary value problems with integral boundary con- ditions for ordinary differential equations arises in different areas of applied mathemat- ics and ...tegral boundary conditions. ... See full document

... of solutions and positive solutions of BVPs for nonlinear FDEs of the following type: functional, evolution, impulsive with integral BCs, can be found in [3, 4, 2, 1, 5, 6, 7, 8, 9, ... See full document

... and lower solution method plays an important role in studying boundary value problems for nonlinear differential equations; see 1 and the references ...to boundary value ... See full document

... of solutions when f satisfies one-sided Nagumo-type ...apply lower and upper functions technique and topological degree method to prove the existence of solutions by making a priori ... See full document

... the method of lower and upper solutions, combined with some Nagumo-type growth condition, which is needed to en- sure an a priori bound for the derivatives of the solutions in order to ... See full document

... functional boundary value problems have been studied by several authors fol- lowing several approaches, as it can be seen, for example, in ...the lower and upper solutions method ... See full document