Your functional interface TestInter does not have corresponding signature for your testStatic(String) method. If you want to refer to testStatic() using the :: notation, you should add the parameter:
interface TestInter2 {
public void abc(String abc);
}
public void runTest () {
TestInter2 demo2 = DemoStatic::testStatic;
demo2.abc(str);
}
According to Oracle Java tutorial, there are four kinds of method reference:

I prepared 3 interfaces - for 0, 1 and 2 parameters. Then we have 3 static and 3 instance methods:
interface F0 {
void f0();
}
interface F1 {
void f1(MetRef i1);
}
interface F2 {
void f2(MetRef i1, MetRef i2);
}
public class MetRef {
public static void stat0() {;}
public static void stat1(MetRef a) {;}
public static void stat2(MetRef a, MetRef b) {;}
public void inst0() {;}
public void inst1(MetRef a) {;}
public void inst2(MetRef a, MetRef b) {;}
}
Now look how each of the methods may be used as a method reference in various combinations, compare them with the previous table. See different method reference types in action and notice from where the parameters come.
public class Test {
public static void main(String[] args) {
final MetRef mr = new MetRef();
final F0 mr01 = MetRef::stat0; // 1: f0() ~ MetRef.stat0()
final F0 mr02 = mr::inst0; // 2: f0() ~ mr.inst0()
final F0 mr04 = MetRef::new; // 4: f0() ~ new MetRef()
final F1 mr11 = MetRef::stat1; // 1: f1(i1) ~ MetRef.stat1(i1)
final F1 mr12 = mr::inst1; // 2: f1(i1) ~ mr.inst1(i1)
final F1 mr13 = MetRef::inst0; // 3: f1(i1) ~ i1.inst0() <== NOTICE!
final F2 mr21 = MetRef::stat2; // 1: f2(i1, i2) ~ MetRef.stat2(i1, i2)
final F2 mr22 = mr::inst2; // 2: f2(i1, i2) ~ mr.inst2(i1, i2)
final F2 mr23 = MetRef::inst1; // 3: f2(i1, i2) ~ i1.inst1(i2) <== NOTICE!
}
}
abcparameter to be withintestStatic? In the lambda expression you're passing instr, which makes perfect sense. You could create an adapter between the two different method signatures (create two functional interfaces, and an adapter which called one based on the other and an extra parameter).DemoStatic::testStatic(str), that's really only a couple keystrokes less than the lambda expression.