This paper is concerned with the existence of positive solutions to singular Dirichlet boundary value problems involving φ -Laplacian. For non-negative nonlinearity f = f ( t , s ) satisfying f ( t , 0 ) ¬ ≡ 0 , the existence of an unbounded solution component is shown. By investigating the shape of the component depending on the behavior of f at ∞ , the existence, nonexistence and multiplicity of positive solutions are studied.
In this study, using a fixed point index theorem on a cone, we present some existence results for one or multiple positive solutions to the m-point boundary value problem with a nonlinear term which does not satisfy the L 1 -Carathéodory condition.
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