Solutions and positive solutions for superlinear Robin problems

An Existence Result of Positive Solutions for Singular Superlinear Boundary Value Problems and Its Applications

GLOBAL STRUCTURE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SECOND ORDER m-POINT BOUNDARY VALUE PROBLEMS

In this paper, we consider the nonlinear eigenvalue problems u′′ + λh(t)f(u) = 0, 0 < t < 1, u(0) = 0, u(1) = m−2 X

Positive and Nodal Solutions for Parametric Nonlinear Robin Problems with Indefinite Potential

We consider a parametric nonlinear Robin problem driven by the p−Laplacian plus an indefinite potential and a Carathéodory reaction which is (p−1)− superlinear without satisfying the Ambrosetti Rabinowitz condition. We prove a bifurcation-type result describing the dependence of the set of positive solutions on the parameter. We also prove the existence of nodal solutions. Our proofs use tools ...

Bifurcation of Positive Solutions for Nonlinear Nonhomogeneous Robin and Neumann Problems with Competing Nonlinearities

In this paper we deal with Robin and Neumann parametric elliptic equations driven by a nonhomogeneous differential operator and with a reaction that exhibits competing nonlinearities (concave-convex nonlinearities). For the Robin problem and without employing the Ambrosetti-Rabinowitz condition, we prove a bifurcation theorem for the positive solutions for small values of the parameter λ > 0. F...

Exact multiplicity of solutions to superlinear and sublinear problems

(f2) lim u→∞ f(u) u =f+ ¿ 0; lim u→−∞ f(u) u =f− ¿ 0: For the de5niteness, we assume f+ ¿f−, and when f+ =f−, we use f± to represent it. We will consider f being either superlinear or sublinear. f is said to be superlinear if f(u)=u is decreasing in (0;∞) and is increasing in (−∞; 0); and f is said to be sublinear if f(u)=u is increasing in (0;∞) and is decreasing in (−∞; 0): The semilinear equ...