Lingju Kong

Positive solutions for a class of higher order boundary value problems with fractional q-derivatives

Abstract The authors study the boundary value problem with fractional q -derivatives - ( D q ν u ) ( t ) = f ( t , u ) , t ∈ ( 0 , 1 ) , ( D q i u ) ( 0 ) = 0 , i = 0 , … , n - 2 , ( D q u ) ( 1 ) = ∑ j = 1 m a j ( D q u ) ( t j ) + λ , where q ∈ ( 0 , 1 ) , m ⩾ 1 and n ⩾ 2 are integers, n - 1 ν ⩽ n , λ ⩾ 0 is a parameter, f : [ 0 , 1 ] × R → [ 0 , ∞ ) is continuous, a i ⩾ 0 and t i ∈ ( 0 , 1 ) for i = 1 , … , m , and D q ν is the q -derivative of Riemann–Liouville type of order ν . The uniqueness, existence, and nonexistence of positive solutions are investigated in terms of different ranges of λ .

UNIQUENESS OF POSITIVE SOLUTIONS OF FRACTIONAL BOUNDARY VALUE PROBLEMS WITH NON-HOMOGENEOUS INTEGRAL BOUNDARY CONDITIONS

The authors study a type of nonlinear fractional boundary value problem with non-homogeneous integral boundary conditions. The existence and uniqueness of positive solutions are discussed. An example is given as the application of the results.

A periodic boundary value problem with vanishing Green's function

Abstract In this work, the authors consider the boundary value problem { y ″ + a ( t ) y = g ( t ) f ( y ) , 0 ≤ t ≤ 2 π , y ( 0 ) = y ( 2 π ) , y ′ ( 0 ) = y ′ ( 2 π ) , and establish the existence of nonnegative solutions in the case where the associated Green’s function may have zeros. The results are illustrated with an example.

Existence and uniqueness of solutions for a fractional boundary value problem on a graph

In this paper, the authors consider a nonlinear fractional boundary value problem defined on a star graph. By using a transformation, an equivalent system of fractional boundary value problems with mixed boundary conditions is obtained. Then the existence and uniqueness of solutions are investigated by fixed point theory.

Positive solutions for third order semipositone boundary value problems

We obtain some sufficient conditions for the existence of positive solutions of a third order semipositone boundary value problem with a multi-point boundary condition. Applications of our results to some special problems are also discussed.

POSITIVE SOLUTIONS OF HIGHER-ORDER BOUNDARY-VALUE PROBLEMS

We consider a class of even-order boundary-value problems with nonlinear boundary conditions and an eigenvalue parameter

Solutions of second order multi-point boundary value problems

\lambda

Positive solutions of boundary value problems for third-order functional difference equations

in the equations. Sufficient conditions are obtained for the existence and non-existence of positive solutions of the problems for different values of

Positive solutions for a semipositone fractional boundary value problem with a forcing term

\lambda

Fractional boundary value problems with integral boundary conditions

.