Using Leray-Schauder degree theory we obtain various existence and multiplicity results for nonlinear boundary value problems φ(u ) = f (t, u, u ), l(u, u ) = 0 where l(u, u ) = 0 denotes the Dirichlet, periodic or Neumann boundary conditions on [0, T ], φ : ]−a, a[ → R is an increasing homeomorphism, φ(0) = 0. The Dirichlet problem is always solvable.For Neumann or periodic boundary conditions, we obtain in particular existence conditions for nonlinearities which satisfy some sign conditions, upper and lower solutions theorems, Ambrosetti-Prodi type results. We prove Lazer-Solimini type results for singular nonlinearities and periodic boundary conditions.

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In this paper, by using Leray-Schauder degree arguments and critical point theory for convex, lower semicontinuous perturbations of C 1 -functionals, we obtain existence of classical positive radial solutions for Dirichlet problems of type div ∇vHere, B(R) = {x ∈ R N : |x| < R} and f : [0, R] × [0, α) → R is a continuous function, which is positive on (0, R] × (0, α).

Abstract. In this paper, using the Schauder fixed point theorem, we prove existence results of radial solutions for Dirichlet problems in the unit ball and in an annular domain, associated to mean curvature operators in Euclidean and Minkowski spaces.

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