Nowadays, linear/nonlinear problems involving partial differential equations have bee became a hot and attractive topics and have been extensively studied, both theoretically and experimentally . Some kinds of boundary conditions coupled with partial differential equatio cause some difficulties in solving such problems. One of the most applied boundary conditions is the nonlocal boundary condition which comes up when values of the unknown function on the boundary are connected to the values inside the domain. In this thesis, after dealing with an approximate method based on the reproducing kernel Hilbert space for solving some partial differential equations such as a pseduparabolic equation and a nonlinear hyperbolic telegraph equation which endowed with a nonlocal boundary condition and an over-specified condition, we present a similar method to solve an inverse problem for parabolic equation with a nonlocal boundary condition and an over-specified condition. The pseduparabolic equation models a variety of important physical processes such as long dispersive waves, the discrepancy between the conductive and thermodynamic temperatures and aggregation of populations. The hyperbolic equation with an integral condition models a Variety of important physical processes such as dynamics of groundwater and population dynamics. The inverse problem for parabolic equation with integral over-specified condition arises from many important applications in heat transfer, termoelasticity, control theory, population dynamics, nuclear reactor dynamics, medical sciences, biochemistry, etc. Reproducing kernel Hilbert space is a very useful and powerful tool of functional analysis with applications in many diverse paradigms such as solving nonlinear partial differential equations. The theory of reproducing kernel was used for the first time at the beginning of the $20$th century by S. Zaremba in his work on boundary value problems for harmonic and biharmonic functions. This theory has been successfully applied for solving ordinary differential equations, partial differential equations, integral equations, integro-differential equations, and so on. In this thesis, firstly, we focus on the definitions and properties of reproducing kernel spaces associated with a brief history of these spaces. Then, the solutions of some partial differential equations such as the pseduparabolic equation, the nonlinear hyperbolic telegraph equation, and an inverse coefficient problem for a parabolic equation, with nonlocal boundary conditions are given in the form of a convergent series with easily computable components, in the reproducing kernel space. The advantages of the approach must lie in the following facts. The approximate solution converges uniformly to the analytical solution. The method is mesh free, easily implemented and capable in treating various boundary conditions. Since the method needs no time discretization, there is no matter, in which time the approximate solution is computed, from the both elapsed time and stability problem, points of view. Also we can evaluate the approximate solution $u_n(x,t)$ for fixed$n$ once, and use it over and over.