A Diophantine problem with a prime and three squares of primes

We prove that if λ1, λ2, λ3 and λ4 are non-zero real numbers, not all of the same sign, λ1/λ2 is irrational, and ϖ is any real number then, for any ε>0, the inequality |λ1p1+λ2p22+λ3p32+λ4p42+ϖ|⩽(maxjpj)−1/18+ε has infinitely many solutions in prime variables p1,…,p4.