We obtain results of existence and multiplicity of solutions for the second-order equation x'' + q(t)g(x) = 0 with x(t) defined for all t in ]0,1[ and such that x(t) goes to infinity as tends to 0+ and to 1-. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0, 1].
Mawhin, J., Papini, D., Zanolin, F. (2003). Boundary blow-up for differential equations with indefinite weight. JOURNAL OF DIFFERENTIAL EQUATIONS, 188(1), 33-51 [10.1016/S0022-0396(02)00073-6].
Boundary blow-up for differential equations with indefinite weight
PAPINI, DUCCIO;
2003-01-01
Abstract
We obtain results of existence and multiplicity of solutions for the second-order equation x'' + q(t)g(x) = 0 with x(t) defined for all t in ]0,1[ and such that x(t) goes to infinity as tends to 0+ and to 1-. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0, 1].
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