[PDF] Top 20 Boundary value problems for singular second order equations

... of singular or non-surjective operators (see [1, 8, ...reaction-diffusion equations with non-constant diffusivity and porous media equations, include mixed differential operators, that is, ... See full document

... As we know, the fixed point theorem of cone expression and compression is extensively used to study the existence of multiple solutions of boundary value problems for second- order ... See full document

... fourth-order boundary value problems of ordinary value problems have important application in various branches of pure and applied ...the boundary value ... See full document

... -point boundary value problem for linear second-order ordinary diffe- rential equations was initiated by Ilin and Moiseev [1] ...multi-point boundary value ... See full document

... differential equations, which arise in biology, physics, population dynamics, economics, and so forth, are a basic tool to study evolution processes that are subjected to abrupt in their states see ...and ... See full document

... In accordance with the method in the proof of Theorem 3.2, we can prove that the boundary value problem (3.20), (3.21) has a unique solution u x   . Denote by u x     T u x     the mapping from ... See full document

... Two consequences of the local minimum theorem were discussed in [] (see [], Sec- tion ). In this section, motivated by [], we state two consequences of Lemma . as follows. The first one is a two critical points ... See full document

... various boundary value problems to show the existence of positive solutions; for example, see 7, 8, 11, 19, 23, ...differential equations by using the fixed point theorem of cone expansion and ... See full document

... Proof We transform the boundary value problem (.) into a fixed point problem, x = Ax, where the operator A is defined by (.). By using the Banach contraction mapping prin- ciple, we shall show that A has ... See full document

... Motivated by [, , –], this paper is concerned with the boundary value problem (.) under sublinear conditions. The method we use is based on some recent fixed point theorems derived by Sun and Liu ... See full document

... Motivated by this, in this paper, we consider the three-point boundary value problem for second-order differential equations (.) and make use of the Leray-Schauder global con- ... See full document

... impulsive singular integro-differential equations in a Banach ...multipoint boundary value problem and nonlinear term permits singularity not only at t 0 but also at x, y, x , y ... See full document

... Since the problem (1.1) cannot transform into a system of second-order equation, the treat- ment method of second-order system does not apply to the problem (1.1). Thus, existing lit- erature ... See full document

... Theorem 3.3. Assume that there exists an ordered couple α, β of a lower and an upper solution for Dirichlet, periodic, or 1.3 conditions. Further, assume that 2.2 and 3.9 hold (and also 3.10, for the 1.3 case). Then the ... See full document

... Remark . Theorem . indicates that the bifurcation interval I = { λ + , λ – }, i.e., problem (.), the bifurcation interval I is a finite point set. What conditions can ensure that the component indeed bifurcates from ... See full document

... differential equations has been widely stud- ied by many scholars in the mathematical sense (see [–] and the references ...periodic boundary value problem were ... See full document

... Singular nonlinear boundary value problems for higher order ordinary differential equations, Nonlin.. Singular boundary value problems, Bull.[r] ... See full document

... Fang, “On positive solutions of boundary value problems for second-order functional di ff erential equations on infinite intervals,” Journal of Mathematical Analysis and Applications , vo[r] ... See full document

... periodic boundary value problems PBVPs for short for second-order ordinary or functional differential equations with or without impulse effects; see 1–24 and the references ... See full document

... Boundary value problems with integral boundary conditions for ordinary differential equations represent a very interesting and important class of problems and arise in the study ... See full document