The article deals with the following boundary value problem
where is a numerical parameter, , . The Euler functional corresponding to this problem is
The authors formulate natural conditions under which the Euler functional is coercive or anticoercive and, as a result, have got the corresponding solvability theorems. Further, they use a modification of the mountain pass lemma and get theorems about the existence of two and three solutions. In the end of the article a simple example is considered.