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Ma, Ruyun; Thompson, Bevan

Nodal solutions for nonlinear eigenvalue problems. (English) Zbl 1059.34013

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 59, No. 5, 707-718 (2004).
Summary: We are concerned with determining values of \(\lambda\), for which there exist nodal solutions of the boundary value problem \[ u''+ ra(t) f(u)= 0,\quad 0< t< 1,\quad u(0)= u(1)= 0. \] The proof of our main result is based upon bifurcation techniques.

Cited in 1 Review
Cited in 38 Documents

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations

Keywords:

Multiplicity results; Eigenvalues; Bifurcation methods; Nodal zeros
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\textit{R. Ma} and \textit{B. Thompson}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 59, No. 5, 707--718 (2004; Zbl 1059.34013)
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References:

[1] Ambrosetti, A.; Hess, P., Positive solutions of asymptotically linear elliptic eigenvalue problems, J. math. anal. appl. (, 73), 2, 411-422, (1980) · Zbl 0433.35026
[2] Elias, U., Eigenvalue problems for the equation \(L_y + \lambda_p(x) y = 0\), J. diff. equations, 29, 28-57, (1978)
[3] Erbe, L.H.; Haiyan Wang, On the existence of positive solutions of ordinary differential equations, Proc. amer. math. soc., 120, 3, 743-748, (1994) · Zbl 0802.34018
[4] Henderson, J.; HaiyanWang, Positive solutions for nonlinear eigenvalue problems, J. math. anal. appl., 208, 252-259, (1997) · Zbl 0876.34023
[5] Naito, Y.; Tanaka, S., On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations, Nonlinear anal. TMA, 56, 4, 919-935, (2004) · Zbl 1046.34038
[6] Rabinowitz, P.H., Nonlinear Sturm-Liouville problems for second order ordinary differential equations, Commun. pure appl. math., 23, 939-961, (1970) · Zbl 0202.08902
[7] Rabinowitz, P.H., Some global results for nonlinear eigenvalue problems, J. funct. anal., 7, 487-513, (1971) · Zbl 0212.16504
[8] Ruf, B.; Srikanth, P.N., Multiplicity results for ODEs with nonlinearities crossing all but a finite number of eigenvalues, Nonlinear anal. TMA, 10, 2, 157-163, (1986) · Zbl 0586.34017
[9] Rynne, B.P., Infinitely many solutions of superlinear fourth order boundary value problems, Topol. methods nonlinear anal., 19, 2, 303-312, (2002) · Zbl 1017.34015
[10] Walter, W., Ordinary differential equations, (1998), Springer New York
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