Positive solutions to superlinear semipositone periodic boundary value problems with repulsive weak singular forces

Positive solutions to superlinear semipositone periodic boundary value problems with repulsive weak singular forces

K e y w o r d s P e r i o d i c boundary value problem, Singular, Positive solutions, Fixed-point theorem in cones. 1. I N T R O D U C T I O N In th is paper , we are devoted to s t u d y the exis tence of posi t ive so lu t ions to per iodic b o u n d a r y value problem, x" + a( t )x = f ( t , x), 0 < t < 1, (I . I) x(0) = x(1), x ' (0) = x ' (1) ; here, a( t ) E L i[0, 1] satisfies t h e con...

Positive Symmetric Solutions of Singular Semipositone Boundary Value Problems

Using the method of upper and lower solutions, we prove that the singular boundary value problem, −u = f(u) u in (0, 1), u(0) = 0 = u(1) , has a positive solution when 0 < α < 1 and f : R → R is an appropriate nonlinearity that is bounded below; in particular, we allow f to satisfy the semipositone condition f(0) < 0. The main difficulty of this approach is obtaining a positive subsolution, whi...

Positive Solutions for Second-Order Singular Semipositone Boundary Value Problems

which arises in many different areas of applied mathematics and physics. Singular problems of this type that the nonlinearity g may change sign are referred to as singular semipositone problems in the literature. Motivated by BVP (1.1), this paper presents the existence results of the following second-order singular semipositone boundary value problem: { u ′′ + f(t, u) + g(t, u) = 0, 0 < t < 1,...

Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

Multiplicity of Positive Periodic Solutions of Singular Semipositone Third-Order Boundary Value Problems

Recommended by Colin Rogers We establish the existence of multiple positive solutions for a singular nonlinear third-order periodic boundary value problem. We are mainly interested in the semipositone case. The proof relies on a nonlinear alternative principle of Leray-Schauder, together with a truncation technique.