PARAMETERS AND SOLUTIONS OF LINEAR AND NONLINEAR OSCILLATORS

ABSTRACT. Relationship between existence of solutions for certain classes of nonlinear boundary value problems and the smallest or the largest eigenvalue of the corresponding linear problem is obtained. Behavior of the solutions, as the parameter increases, is also studied. KEY WORDS AND PHRASES. Eistence of solutions, nnear boundy value probem, elgenvdlus, boundedness of sotions and parameters. AMS (MOS) SUBJECT CLASSIFICATION (1970) CODES. 34B15, 34B25. I. INTRODUCTION. Equations of the form y"(x) + p(x) y(x) + %q(x) yn(x) 0 where % is a parameter and n is a positive integer, arise in many physical problems