Positive solutions of the conjugate boundary value problem.
Positive solutions of three-point boundary value problems for higher-order -Laplacian with infinitely many singularities.
Positive solutions of three-point boundary-value problems for p-Laplacian singular differential equations.
Positive solutions of three-point nonlinear second order boundary value problem.
Positive solutions to a boundary-value problem for second order ordinary differential equations.
Positive solutions to a class of elastic beam equations with semipositone nonlinearity
Let h ∈ L¹[0,1] ∩ C(0,1) be nonnegative and f(t,u,v) + h(t) ≥ 0. We study the existence and multiplicity of positive solutions for the nonlinear fourth-order two-point boundary value problem , 0 < t < 1, u(0) = u’(0) = u’(1) =u”’(1) =0, where the nonlinear term f(t,u,v) may be singular at t=0 and t=1. By constructing a suitable cone and integrating certain height functions of f(t,u,v) on some bounded sets, several new results are obtained. In mechanics, the problem models the deflection of...
Positive solutions to a generalized second-order three-point boundary-value problem on time scales.
Positive solutions to a nonlinear third order three-point boundary value problem.
Positive solutions to a second-order multi-point boundary-value problem.
Positive solutions to a singular fourth-order two-point boundary value problem
This paper studies the existence of multiple positive solutions to a nonlinear fourth-order two-point boundary value problem, where the nonlinear term may be singular with respect to both time and space variables. In order to estimate the growth of the nonlinear term, we introduce new control functions. By applying the Hammerstein integral equation and the Guo-Krasnosel'skii fixed point theorem of cone expansion-compression type, several local existence theorems are proved.
Positive solutions to an th order right focal boundary value problem.
Positive solutions to boundary value problems of nonlinear fractional differential equations.
Positive solutions to generalized second-order three-point integral boundary-value problems.
Positive solutions to nonlinear first-order nonlocal BVPs with parameter on time scales.
Positive solutions to nonlinear higher-order nonlocal boundary value problems for fractional differential equations.
Positive solutions to systems of nonlinear second order three-point boundary value problems.
Positive solutions with given slope of a nonlocal second order boundary value problem with sign changing nonlinearities
We study a nonlocal boundary value problem for the equation x''(t) + f(t,x(t),x'(t)) = 0, t ∈ [0,1]. By applying fixed point theorems on appropriate cones, we prove that this boundary value problem admits positive solutions with slope in a given annulus. It is remarkable that we do not assume f≥0. Here the sign of the function f may change.
Positive symmetric solutions of singular semipositone boundary value problems.
Positivity conditions and bounds for Green’s functions for higher order two-point BVP
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear equations are also discussed.
Properties of the set of positive solutions to Dirichlet boundary value problems with time singularities
The paper investigates the structure and properties of the set S of all positive solutions to the singular Dirichlet boundary value problem u″(t) + au′(t)/t − au(t)/t 2 = f(t, u(t),u′(t)), u(0) = 0, u(T) = 0. Here a ∈ (−∞,−1) and f satisfies the local Carathéodory conditions on [0,T]×D, where D = [0,∞)×ℝ. It is shown that S c = {u ∈ S: u′(T) = −c} is nonempty and compact for each c ≥ 0 and S = ∪c≥0 S c. The uniqueness of the problem is discussed. Having a special case of the problem, we introduce...