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

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

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 Boundary-value Problems with Derivative Dependence on Finite and Infinite Intervals

In this paper, Krasnoselskii’s theorem and the fixed point theorem of cone expansion and compression are improved. Using the results obtained, we establish the existence of multiple positive solutions for the singular second-order boundary-value problems with derivative dependance on finite and infinite intervals.

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 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...