Exact number of positive solutions for semipositone problems
نویسندگان
چکیده
منابع مشابه
Positive Solutions for a Class of Infinite Semipositone Problems
We analyze the positive solutions to the singular boundary value problem −∆u = λ[f(u)− 1/u];x ∈ Ω u = 0; x ∈ ∂Ω, where f is a C function in (0,∞), f(0) ≥ 0, f ′ > 0, lims→∞ f(s) s = 0, λ is a positive parameter, α ∈ (0, 1) and Ω is a bounded region in R, n ≥ 1 with C boundary for some γ ∈ (0, 1). In the case n = 1 we use the quadrature method and for n > 1 we use the method of sub-super solutio...
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which arises in many different areas of applied mathematics and physics. Singular problems of this type that the nonlinearity g may change sign are referred to as singular semipositone problems in the literature. Motivated by BVP (1.1), this paper presents the existence results of the following second-order singular semipositone boundary value problem: { u ′′ + f(t, u) + g(t, u) = 0, 0 < t < 1,...
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We consider the uniqueness of the positive solution to a semilinear elliptic equation with Dirichlet boundary condition and the nonlinearity satisfying f(0) < 0 and having asymptotic sublinear growth rate. A similar idea is also applied to the nonexistence of a positive solution to a superlinear problem.
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Using the method of upper and lower solutions, we prove that the singular boundary value problem, −u = f(u) u in (0, 1), u(0) = 0 = u(1) , has a positive solution when 0 < α < 1 and f : R → R is an appropriate nonlinearity that is bounded below; in particular, we allow f to satisfy the semipositone condition f(0) < 0. The main difficulty of this approach is obtaining a positive subsolution, whi...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2006
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2005.09.043