Existence of Solutions of Nonlinear Mixed Two-Point Boundary Value Problems for Third-Order Nonlinear Differential Equation

Abstract

The authors use the upper and lower solution method to study the existence of solutions of nonlinear mixed two-point boundary value problems for third-order nonlinear differential equation$y\mathrm{\prime \prime \prime }=f(x,y,y\prime ,y\mathrm{\prime \prime }),y\prime (b)=h(y\prime (a)),p(y(a),y(b),y\prime (a),y\prime (b))=0,g(y(a),y(b),y\prime (a),y\prime (b),y\mathrm{\prime \prime }(a),y\mathrm{\prime \prime }(b))=0$. Some new existence results are obtained by developing the upper and lower solution method. Some applications are also presented.