کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
843828 908566 2007 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Existence and nonexistence of solutions of second-order nonlinear boundary value problems
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Existence and nonexistence of solutions of second-order nonlinear boundary value problems
چکیده انگلیسی

We study the nonlinear boundary value problem consisting of the equation −y″+q(t)y=w(t)f(y) on [a,b]−y″+q(t)y=w(t)f(y) on [a,b] and a general separated homogeneous linear boundary condition. By comparing this problem with a corresponding linear Sturm–Liouville problem we obtain conditions for the existence and nonexistence of solutions of this problem. More specifically, let λn,n=0,1,2,…λn,n=0,1,2,…, be the nn-th eigenvalues of the corresponding linear Sturm–Liouville problem. Then under certain assumptions, the boundary value problem has a solution with exactly nn zeros in (a,b)(a,b) if λnλn is in the interior of the range of f(y)/y,y∈(0,∞)f(y)/y,y∈(0,∞); and does not have any solution with exactly nn zeros in (a,b)(a,b) if λnλn is outside of the range of f(y)/y,y∈(0,∞)f(y)/y,y∈(0,∞). These conditions become necessary and sufficient when f(y)/yf(y)/y is monotone. The existences of multiple and even an infinite number of solutions are derived as consequences. We also discuss the changes of the number and the types of nontrivial solutions as the interval [a,b][a,b] shrinks, as qq increases in a given direction, and as the boundary condition changes.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 66, Issue 11, 1 June 2007, Pages 2635–2651
نویسندگان
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