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Existence and multiplicity of positive solutions for nonlinear boundary value problems with a parameter. (English) Zbl 1229.34036

Summary: The nonlinear boundary value problem

-(p(t)u ' ) ' +q(t)u=λf(t,u),0tω,u(0)=u(ω),p(0)u ' (0)=p(ω)u ' (ω),

is studied. By using the fixed point index theory, some existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values of λ. The results obtained herein generalize and improve the results in the literature.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B08Parameter dependent boundary value problems for ODE
47N20Applications of operator theory to differential and integral equations
34B15Nonlinear boundary value problems for ODE
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