Multiplicity of Solutions to Nonlinear Boundary Value Problem with Nonlocal Boundary Condition

In this paper the author considers the following nonlinear boundary value problem with nonlocal boundary conditions$[left{ begin{array}{l}Lu equiv - sumlimits_{i,j = 1}^n {frac{partial }{{partial {x_i}}}({a_{ij}}(x)frac{{partial u}}{{partial {x_j}}}) = f(x,u,t)} u{|_Gamma } = const, - int_Gamma {sumlimits_{i,j = 1}^n {{a_{ij}}frac{{partial u}}{{partial {x_j}}}cos (n,{x_i})ds = 0} }end{array} right.]$Under suitable assumptions on f it is proved that there exists $t_0in R,-infinityt_0, at least one solution at t=t_0 at least two solutions as t