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Multiplicity results for a third order boundary value problem at resonance. (English) Zbl 0932.34014
The author deals with the boundary value problem \[ x'''+ k^2x'+ g(x,x')= p(t),\quad x'(0)= x'(\pi)= x(\eta)= 0, \] where \(\eta\) is fixed, and the nonlinearity \(g\) is bounded. Existence and nonuniqueness of solutions are studied together with the structure of the solution set.

34B15 Nonlinear boundary value problems for ordinary differential equations
Full Text: DOI
[1] Nagle, R.K.; Pothoven, K.L., On a third order nonlinear boundary value problem at resonance, J. math. anal. appl., 195, 149-159, (1995) · Zbl 0847.34026
[2] Gupta, C.P., On a third-order boundary value problem at resonance, Differential integral equations, 2, 1-12, (1989) · Zbl 0722.34014
[3] Aftabizadeh, A.R.; Gupta, C.P.; Xu, J.M., Existence and uniqueness theorems for three point boundary value problem, SIAM J. math. anal., 20, 716-720, (1989) · Zbl 0704.34019
[4] O’Reagan, D.J., Topological transversality: applications to third order boundary value problems, SIAM J. math. anal., 19, 630-641, (1987) · Zbl 0628.34017
[5] Martelli, M.; Vignoli, A., On the structure of the solution set of nonlinear equations, Nonlinear analysis, 7, 7, 685-693, (1983) · Zbl 0519.47037
[6] Costa, D.G.; Concalves, J.V.A., Existence and multiplicity results for a class of nonlinear elliptic boundary value problem at resonance, J. math. anal. appl., 84, 328-337, (1981) · Zbl 0479.35037
[7] Fucik, S., Solvability of nonlinear equations and boundary value problems, (1980), D. Reidel Dordrecht · Zbl 0453.47035
[8] Ambrosetti, A.; Mancini, G., Existence and multiplicity results for nonlinear elliptic problem with linear part at resonance. the case of the simple eigenvalues, J. differential equations, 28, 220-245, (1978) · Zbl 0393.35032
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