You know… Your favorite answers (No, Nope) are neither helpful nor friendly nor explanatory nor always correct.
Define "running on higher resolution" first.
Many DS games are 2D, using sprites. They cannot be just rendered in higher resolution like 3D games. Even using PC emulators and filters like HQ (or whatever they are called) you won't get more detail or 100% smooth HD graphics out of low-res 2D games. So technically the answer to really run (render) DS games at higher resolution on 3DS is "no". But that answer falls short because there are possibilities to adjust/tweak/optimize(?) the output.
So…
The resolution of the DS(i) is 256×192 for both screens while the 3DS family has 400¹×240 for the upper screen and 320×240 for the lower screen. Obviously the 3DS has to do some upscaling to fill the screens to 320×240. By holding (Select) or (Start) on starting a DS(i) game you can disable that and run the older games pixel perfect (and pretty small).
Since the resolution 3DS compared to DS isn't that much higher and not a multiple of the original, upscaling is limited and will always look somewhat blurry. You can try
patching the upscaler and see what mode suits you the most. There are possibilities to run many DS games in widescreen mode with that as well.