Find in Library
Search millions of books, articles, and more
Indexed Open Access Databases
Nodal Solutions for a Class of Fourth-Order Two-Point Boundary Value Problems
oleh: Xu Jia, Han XiaoLing
Format: | Article |
---|---|
Diterbitkan: | SpringerOpen 2010-01-01 |
Deskripsi
<p/> <p>We consider the fourth-order two-point boundary value problem <inline-formula> <graphic file="1687-2770-2010-570932-i1.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2010-570932-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2010-570932-i3.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2010-570932-i4.gif"/></inline-formula> is a parameter, <inline-formula> <graphic file="1687-2770-2010-570932-i5.gif"/></inline-formula> is given constant, <inline-formula> <graphic file="1687-2770-2010-570932-i6.gif"/></inline-formula> with <inline-formula> <graphic file="1687-2770-2010-570932-i7.gif"/></inline-formula> on any subinterval of <inline-formula> <graphic file="1687-2770-2010-570932-i8.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2010-570932-i9.gif"/></inline-formula> satisfies <inline-formula> <graphic file="1687-2770-2010-570932-i10.gif"/></inline-formula> for all <inline-formula> <graphic file="1687-2770-2010-570932-i11.gif"/></inline-formula>, and <inline-formula> <graphic file="1687-2770-2010-570932-i12.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2010-570932-i13.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2010-570932-i14.gif"/></inline-formula> for some <inline-formula> <graphic file="1687-2770-2010-570932-i15.gif"/></inline-formula>. By using disconjugate operator theory and bifurcation techniques, we establish existence and multiplicity results of nodal solutions for the above problem.</p>