rofl " thid party support is strong" 

what planet did you came from

That's the thing though. This was actually a common prediction from analysts and Sony themselves, because the PSP was destined to put an end to Nintendo's dominance in the portable space, just like the original PlayStation dethroned Nintendo in the home console arena. After history has taken its course and the underpowered DS crushed the mighty PSP, history is rewritten in the context of an unbeatable Nintendo and a very respectable foray for Sony in the portable gaming market. Why do you think did the DS start out with poor third party support while the PSP had pretty much every major publisher on board? Because analysts forecasted the imminent end of Nintendo's domination.

There is a famous quote from Phil Harrison who says that it's just not fair to compare the PSP and DS, with the implication that Sony is far superior. Who else other than the companies themselves set the bar for success?

The PSP also weakened trust and faith in Sony as a whole. Before the PSP, Sony had a flawless track record in the video games market, but now everyone could see that they are vulnerable which adds to the reasons why third parties didn't hesitate to move their games multiplatform. PlayStation was no longer a safe bet for the industry.

But due the most favorable turns of events, the PSP still ended up being moderately successful. It wasn't Sony who brought the platform back to life though. The failure of the PS3, the hate for the Wii and the general movement towards handheld gaming in the Japanese market along with the surprise hit Monster Hunter led to a shift in third party support. The PS3 was too expensive to develop for and had a small userbase. The 360 was in an even worse position and, due its abysmal installed base, going HD multiplatform wouldn't have made a difference to the problem. Nobody liked the Wii. The DS lacked the horsepower to take over from everything that was possible on the PS2, the previous lead platform for Japanese game development. So after the PS2 faded away, there was only one option left: the PSP. And it got the majority of games which is precisely why it has a long tail like a generational leader in Japan and the DS had not, because it was slowly abandoned a couple of years ago.