One can be influenced by the demons without being possessed since we live in a world governed by them... to the Ephesians, Paul said in Ephesians 2:2,3...
“in which you at one time walked according to the system of things of this world, according to the ruler of the authority of the air, the spirit that is now at work in the sons of disobedience. Yes, among them we all at one time conducted ourselves in harmony with the desires of our flesh, carrying out the will of the flesh and of our thoughts, and we were naturally children of wrath just as the rest."
The world’s 'air,' or spirit, is an invisible, impelling force that incites disobedience to God and fosters “the desire of the flesh and the desire of the eyes.”1 John 2:16; 1 Timothy 6:9, 10
“The authority” of this spirit lies in its appeal to the sinful flesh, its subtlety, its relentlessness and, like air, its pervasiveness.