I installed a 4 foot wall between my new kitchen and dining room I used 2x4 I screwed it to the floor but it still seems wobbly how can I strengthing it up

Assuming this wall is a 4 High wall, Did you use a bottom plate on the old floor then studs. If not right there is the first problem.

The best way for a Knee wall is to build the wall first so you can screw through the bottom of the plate and then set wall and screw plate to floor. Keep in mind the sud cuts because you want a Double plate on the top of that wall for stiffness. I like 12"O.C. studs for that application for better stiffness.

The other thing is a 2x4 wall width is not as good as a 2x6 width simply because if the rocking is less on a 2x6 base/plate.

Now if this is just a 4 foot long wall 8 feet high you still need a top and bottom plate for rigidity. Explain the wobble here and stud centers

Assuming this wall is a 4 High wall, Did you use a bottom plate on the old floor then studs. If not right there is the first problem.

The best way for a Knee wall is to build the wall first so you can screw through the bottom of the plate and then set wall and screw plate to floor. Keep in mind the sud cuts because you want a Double plate on the top of that wall for stiffness. I like 12"O.C. studs for that application for better stiffness.

The other thing is a 2x4 wall width is not as good as a 2x6 width simply because if the rocking is less on a 2x6 base/plate.

Now if this is just a 4 foot long wall 8 feet high you still need a top and bottom plate for rigidity. Explain the wobble here and stud centers

I built wall on floor with top and bottom board and lift in to place and attached it to the wall on one end but the other end is stiil kind of shaky

Once you cover the wall with drywall it will get more les wobbly.