Multiple positive solutions of nonlinear BVPs for differential systems involving integral conditions

作者：Zhang Hai E^*

来源：Boundary Value Problems, 2014, 2014(1): 61.

DOI：10.1186/1687-2770-2014-61

• differential system
• multiple positive solution
• integral conditions

In this paper, we consider the following system of nonlinear third-order nonlocal boundary value problems (BVPs for short):
{-u'''(t) = f(t, v(t), v'(t)), t is an element of (0, 1),
-v'''(t) = g(t, u(t), u'(t)), t is an element of (0, 1),
u(0) = 0, au'(0)-bu ''(0) = alpha[u], cu'(1) + du ''(1) = beta[u], v(0) = 0, av'(0)-bv ''(0) = alpha[v], cv'(1) + dv ''(1) = beta[v],
where f, g is an element of C([0, 1] x R+ x R+, R+), alpha[u] = integral(1)(0) u(t) dA(t) and beta[u] = integral(1)(0) u(t) dB(t) are linear functionals on C[0, 1] given by Riemann- Stieltjes integrals and are not necessarily positive functionals; a, b, c, d are nonnegative constants with rho := ac + ad + bc > 0. By using the Guo- Krasnoselskii fixed point theorem, some sufficient conditions are obtained for the existence of at least one or two positive solutions and nonexistence of positive solutions to the above problem. Two examples are also included to illustrate the main results.

• 出版日期2014-3-21
• 单位唐山学院