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...
Radial positive solutions for a nonpositone problem in a ball.
Results for twin singular nonlinear problems with damping term.
Semiclassical states for weakly coupled nonlinear Schrödinger systems
We consider systems of weakly coupled Schrödinger equations with nonconstant potentials and investigate the existence of nontrivial nonnegative solutions which concentrate around local minima of the potentials. We obtain sufficient and necessary conditions for a sequence of least energy solutions to concentrate.
Semipositone -point boundary-value problems.
Several existence theorems of monotone positive solutions for third-order multipoint boundary value problems.
Several existence theorems of multiple positive solutions of nonlinear -point BVP for an increasing homeomorphism and homomorphism on time scales.
Several existence theorems of nonlinear -point BVP for an increasing homeomorphism and homomorphism on time scales.
Singular higher order boundary value problems for ordinary differential equations.
Singular nonlinear problem for ordinary differential equation of the second order
The paper deals with the singular nonlinear problem where , . We prove the existence of a solution to this problem which is positive on under the assumption that the function is nonnegative and can have time singularities at , and space singularity at . The proof is based on the Schauder fixed point theorem and on the method of a priori estimates.
Singular positone and semipositone boundary value problems of nonlinear fractional differential equations.
Singular -Laplacian third-order BVPs with derivative dependance
This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a -Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition is assumed....