Existence theorems of nonlinear asymptotic BVP for a homeomorphism (original) (raw)

Existence of Positive Unbounded Solutions for Φ-Laplacian BVPS on the Half Line

International Electronic Journal of Pure and Applied Mathematics, 2013

We provide in this work sufficient conditions for existence of positive unbounded solutions to the boundary value problem    − (φ (u ′)) ′ = a(t)f (t, u), t ∈ (0, +∞) , u (0) = 0, lim t→+∞ u ′ (t) = 0 where φ : R + → R + is an increasing homeomorphism with φ (0) = 0, a : (0, +∞) → R + is a measurable function which does not vanish identically on (0, +∞) and the function f : R + × R + → R + is continuous.

Nonhomogeneous boundary value problems for some nonlinear equations with singular ϕ-Laplacian

Journal of Mathematical Analysis and Applications, 2009

Using Leray-Schauder degree theory we obtain various existence results for the quasilinear equation problems φ(u) = f (t, u, u) submitted to nonhomogeneous Dirichlet or nonlinear Neumann-Steklov boundary conditions on [0, T ], when φ : ]−a, a[ → R is an increasing homeomorphism, φ(0) = 0. We compare the results with the ones proved earlier in the homogeneous case.

Topological structure of solution sets to asymptotic boundary value problems

Journal of Differential Equations, 2010

Topological structure is investigated for second-order vector asymptotic boundary value problems. Because of indicated obstructions, the R δ -structure is firstly studied for problems on compact intervals and then, by means of the inverse limit method, on noncompact intervals. The information about the structure is furthermore employed, by virtue of a fixed-point index technique in Fréchet spaces developed by ourselves earlier, for obtaining an existence result for nonlinear asymptotic problems. Some illustrating examples are supplied.

Global curve of positive solutions for φ - Laplacian Dirichlet bvp with at most one turning point

Differential Equations & Applications, 2013

Under suitable conditions we prove that the set of positive solutions to the ϕ− Laplacian boundary value problem −(ϕ(u)) = λ f (u) in (0,1); u(0) = u(1) = 0, where λ > 0 is a real parameter, ϕ is an odd increasing homeomorphism of R and f ∈ C([0,+∞),[0,+∞)), consists on a curve u → λ (u). λ > 0 is a real parameter, ϕ is an odd increasing homeomorphism of R and f : R + → R + is continuous where R + = [0, +∞). In all this paper we assume that f (u) > 0 for all u > 0.

A Dirichelet–Neumann m-point BVP with a p-Laplacian-like operator

Nonlinear Analysis: Theory, Methods & Applications, 2005

Let , be odd increasing homeomorphisms from R onto R satisfying (0) = (0) = 0, and let f : [a, b] × R × R → R be a function satisfying Carathéodory's conditions. Let i ∈ R, i ∈ (a, b), i =1,. .. , m−2, a < 1 < 2 < • • • < m−2 < b be given. We are interested in the problem of existence of solutions for the m-point boundary value problem: