Positive solutions of second order semipositone singular three-point boundary value problems.
Positive solutions of second-order singular boundary value problem with a Laplace-like operator.
Positive solutions of singular fourth-order boundary-value problems.
Positive solutions of some higher order nonlocal boundary value problems.
Positive solutions of some nonlocal boundary value problems.
Positive solutions of systems of boundary value problems.
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 two-point right focal eigenvalue problems on time scales.
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 nonlinear third order three-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 nonlinear second-order three-point boundary-value problems for difference equation with change of sign.
Positive solutions to nonlinear singular second order boundary value problems
Existence theorems of positive solutions to a class of singular second order boundary value problems of the form y'' + f(x,y,y') = 0, 0 < x < 1, are established. It is not required that the function (x,y,z) → f(x,y,z) be nonincreasing in y and/or z, as is generally assumed. However, when (x,y,z) → f(x,y,z) is nonincreasing in y and z, some of O'Regan's results [J. Differential Equations 84 (1990), 228-251] are improved. The proofs of the main theorems are based on a fixed point theorem for...
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.