Positive Solutions for a Singular Superlinear Fourth-Order Equation with Nonlinear Boundary Conditions

الملخص EN

We show the existence of positive solutions for a singular superlinear fourth-order equation with nonlinear boundary conditions.

u⁗x=λhxfux, x∈0,1,u0=u′0=0,u″1=0, u⁗1+cu1u1=0, where λ > 0 is a small positive parameter, f:0,∞⟶ℝ is continuous, superlinear at ∞, and is allowed to be singular at 0, and h: [0, 1] ⟶ [0, ∞) is continuous.

Our approach is based on the fixed-point result of Krasnoselskii type in a Banach space.