I am trying to make some grass. I want to have grass only near the edges of my plane and not on the center.
Is any way to do that?
Or I have to split the plane and make different objects?

You can use Vertex Groups.
Subdivide your plane (W> Subdivide)

Deselect the middle with Circle select (C) and use MMB to deselect (or hold Shift and use LMB)

Add a vertex group and click Assign in Properties > Object data > Vertex Groups:

Select the vertex group in Properties > Particles > Vertex Groups:

You can also use a Particle Texture. This does not require that you subdivide your mesh.
Add a particle texture to your object by clicking New in Properties > Particle system > Textures. Then switch to the texture tab.
Ensure that the the datablock type is set to Particle system.
Set the texture type to Blend
Set the Progression to Sphere
Enable Density in the Influence section so the texture influences the density of the particles.
Enable Ramp to control the texture with a color ramp.
Flip the ramp and adjust the stops so the particles are correctly placed.

In addition to the other answer. You can also do Ctrl+Shift to go into weight painting mode and then paint on a heat map, the parts you paint red will be the parts that will have hair particles on the mesh.
Don't forget to set group as the density for the particle system.
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