Positive solutions for a concave semipositone Dirichlet problem

Two positive solutions of a quasilinear elliptic Dirichlet problem

For a class of second order quasilinear elliptic equations we establish the existence of two non-negative weak solutions of the Dirichlet problem on a bounded domain, Ω. Solutions of the boundary value problem are critical points of C−functional on H 0 (Ω). One solution is a local minimum and the other is of mountain pass type. Mathematics Subject Classification (2000). Primary 35J62; Secondary...

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...

Existence of symmetric positive solutions for a semipositone problem on time scales

This paper studies the existence of symmetric positive solutions for a second order nonlinear semipositone boundary value problem with integral boundary conditions by applying the Krasnoselskii fixed point theorem. Emphasis is put on the fact that the nonlinear term f may take negative value. An example is presented to demonstrate the application of our main result.

Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractional q-Derivatives Equation

and Applied Analysis 3 The q-integral of a function f defined in the interval [0, b] is given by

Research Article Positive Solutions for Two-Point Semipositone Right Focal Eigenvalue Problem