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Displaying 41 –
60 of
111
We discuss the existence of positive radial solutions of the semilinear elliptic equation
⎧-Δu = K(|x|)f(u), x ∈ Ω
⎨αu + β ∂u/∂n = 0, x ∈ ∂Ω,
⎩,
where , N ≥ 3, K: [r₀,∞) → ℝ⁺ is continuous and , f ∈ C(ℝ⁺,ℝ⁺), f(0) = 0. Under the conditions related to the asymptotic behaviour of f(u)/u at 0 and infinity, the existence of positive radial solutions is obtained. Our conditions are more precise and weaker than the superlinear or sublinear growth conditions. Our discussion is based on the fixed point...
Existence principles for solutions of singular differential systems satisfying nonlocal boundary conditions are stated. Here is a homeomorphism onto and the Carathéodory function may have singularities in its space variables. Applications of the existence principles are given.
New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.
We present a generalized degree theory for continuous maps f: (D, ∂D) → (E, E0), where E is a normed vectorial space, D is an open subset of Rk x E such that p1(D) is bounded in Rk and f is a compact perturbation of the second projection p2: Rk x E → E.
We consider a reaction-diffusion system of activator-inhibitor type which is subject to Turing's diffusion-driven instability. It is shown that unilateral obstacles of various type for the inhibitor, modeled by variational inequalities, lead to instability of the trivial solution in a parameter domain where it would be stable otherwise. The result is based on a previous joint work with I.-S. Kim, but a refinement of the underlying theoretical tool is developed. Moreover, a different regime of parameters...
A homology theory of Banach manifolds of a special form, called FSQL-manifolds, is developed, and also a homological degree of FSQL-mappings between FSQL-manifolds is introduced.
In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.
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