Positive solutions for nonlinear nth-order singular eigenvalue problem with nonlocal conditions

The nonlinear nth-order singular nonlocal boundary value problem

     

Positive periodic solutions of Hill’s equations with singular nonlinear perturbations

We study the existence and multiplicity of positive periodic solutions of Hill’s equations with singular nonlinear perturbations. The new results are applicable to the case of a strong singularity as well as the case of a weak singularity. The proof relies on a nonlinear alternative principle of Leray–Schauder and a fixed point theorem in cones. Some recent results in the literature are generalized and improved.     

Positive solutions for mixed problems of singular fractional differential equations

We investigate the existence of positive solutions to the singular fractional boundary value problem: $^c\hspace{-1.0pt}D^{\alpha }u +f(t,u,u^{\prime },^c\hspace{-2.0pt}D^{\mu }u)=0$, u′(0) = 0, u(1) = 0, where 1 < α < 2, 0 < μ < 1, f is a L^q‐Carathéodory function, $q > \frac{1}{\alpha -1}$, and f(t, x, y, z) may be singular at the value 0 of its space variables x, y, z. Here $^c \hspace{-1.0pt}D$ stands for the Caputo fractional derivative. The results are based on combining regularization and sequential techniques with a fixed point theorem on cones.     

The existence of countably many positive solutions for singular multipoint boundary value problems

In this paper, we study the existence of countably many positive solutions for a singular multipoint boundary value problem. By using fixed-point index theory and the Leggett-Williams’ fixed-point theorem, sufficient conditions for the existence of countably many positive solutions are established.     

Optimal conditions of solvability of nonlocal problems for second-order ordinary differential equations

For the differential equation

u^″=f(t,u)     

Existence of multiple positive solutions of singular nonlinear boundary value problems

For a given positive integer N, we provide conditions on the nonlinear function f which guarantee that the boundary value problem

     

Singular Dirichlet second-order BVPs with impulses

The paper deals with the existence of solutions to singular second-order differential equations with impulse effects and with the Dirichlet boundary conditions. The right-hand side of the differential equation can be singular in its phase variable.     

On the existence of periodic solutions for the third-order nonlinear ordinary differential equations

In this paper,the existence of periodic solution for the third-order nonlinear ordinarydifferential equation of the form -^x f(-^x) g(-^x) h(x)=p(t) is consldered,where f,g,h andp are the continuous functlons, and p (t T) =p (t). By using the Leray-Schauder degreemethod,some sufficient conditions to guarantee the existence of T periodic solution for the equation are obtained. Some previous results are extended and improved.     

Positive solutions for 2p-order and 2q-order systems of singular boundary value problems with integral boundary conditions

In this paper, we study the existence, multiplicity and nonexistence of positive solutions for 2p-order and 2q-order systems of singular boundary value problems with integral boundary conditions. The results are based upon the fixed-point theorem of cone expansion and compression type due to Krasnosel’skill. Moreover, it generalizes and includes some known results.