Justino Sánchez

Uniqueness results for the one-dimensional m-Laplacian considering superlinear nonlinearities

Abstract We study existence and uniqueness of positive solutions of the boundary value problem ( P ) λ −(|u′| m−2 u′)′=λf(u) in (0,1), u(0)=u(1)=0, where λ is a positive parameter, m>1, and f:[0,+∞)→ R is a continuous function which vanishes at most once in (0,+∞). Assuming that f is superlinear at +∞, we study its behavior near zero to obtain uniqueness results, which are proved using the shooting method.

Positive solutions for some nonlocal and nonvariational elliptic systems

Using fixed point techniques, we study the existence and multiplicity of positive radial solutions for two classes of nonlocal elliptic systems defined on bounded annular domains or exterior domains. To this end, we reduce our problem to second-order functional ordinary elliptic systems. Our approach also allows us to study systems involving various orders, which serve as models for the suspension bridge equations.

Positive solutions for certain classes of fourth-order ordinary elliptic systems

Using fixed-point techniques, we study the existence of positive solutions for a class of fourth-order ordinary elliptic systems. To this end, we reduce our problem to an appropriate functional differential equation.