Existence of solutions of boundary value problems for nonlinear second order systems in a Banach space

Problems with Mixed Boundary Conditions in Banach Spaces

“…In [3], the nonlinear term ( , , ) is bounded; in our result, the nonlinear term ( , , ) may possess no more than linear growth. Now we consider an example to illustrate our results.…”

“…The existence of solutions for second-order boundary value problems has been studied by many authors using various methods (see [1][2][3][4][5][6]). …”

“…Recently, Zhou and Peng [5] have studied the following boundary value problem: − = ( , ) , (0) = 0 = (1) , (3) where : [0, 1] × → is a continuous function and is a Banach space. They obtained the existence of solutions of (3), where the main tools used in the study are Sadovskii fixed point theorem and precise computation of measure of noncompactness.…”

“…They obtained the existence of solutions of (3), where the main tools used in the study are Sadovskii fixed point theorem and precise computation of measure of noncompactness.…”

Nonnegative solutions of two‐point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

“…In [1] (see also [21 Section 5.3), several existence theorems were established for the BVP of nonlinear second order differential equation in Banach space" -x"= f(t,x,x'), 0 < t <_ 1; (1) ax(O) bx'(O) = Zo, cx(1)+ dx'(1) = x. Now, in this paper, we shall combine the fixed point theory, fixed point index theory and cone theory to extend some results of [1] …”