On the Existence of Multiple Positive Solutions for a Semilinear Problem in Exterior Domains

On the Existence of Multiple Positive Solutions for a Semilinear Problem in Exterior Domains

In this paper, we study the existence and nonexistence of multiple positive solutions for problem   ∆u+K(x)up = 0 in Ω. u > 0 in Ω, u ∈ H1 loc(Ω) ∩ C(Ω). u ∣∣ ∂Ω = 0, u → μ > 0 as |x| → ∞ where Ω = RN \ ω is an exterior domain in RN , ω ⊂ RN is a bounded domain with smooth boundary and N > 2. μ ≥ 0, p > 1 are some given constants. K(x) satisfies: K(x) ∈ Cα loc(Ω) and ∃C, ,M > 0 such t...

Multiple Positive Solutions of Semilinear Elliptic Problems in Exterior Domains

Existence of positive solutions for a boundary value problem of a nonlinear fractional differential equation

This paper presents conditions for the existence and multiplicity of positive solutions for a boundary value problem of a nonlinear fractional differential equation. We show that it has at least one or two positive solutions. The main tool is Krasnosel'skii fixed point theorem on cone and fixed point index theory.

Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also, by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.

Existence of Multiple Periodic Solutions for a Semilinear Evolution Equation

In this paper, we consider the existence of multiple periodic solutions for the problem du , . , — +Lu = g(u) + h, r>0, dt "(0) = u(T), where L is a uniformly strongly elliptic operator with domain D(L) = Hjf(Q), g: R —► R is a continuous mapping, T > 0 and h: (0,T) —> HTM(Q.) is a measurable function.