Existence theory for single and multiple solutions to semipositone discrete Dirichlet boundary value problems with singular dependent nonlinearities

Existence Theory for Single and Multiple Solutions to Semipositone Discrete Dirichlet Boundary Value Problems with Singular Dependent Nonlinearities

In this paper we establish the existence of single and multiple solutions to the semiposi-tone discrete Dirichlet boundary value problem ∆ 2 y(i − 1) + µf (i, y(i)) = 0, i ∈ {1, 2, ..., T } y(0) = y(T + 1) = 0, where µ > 0 is a constant and our nonlinear term f (i, u) may be singular at u = 0. .

Existence of multiple solutions for Sturm-Liouville boundary value problems

In this paper, based on variational methods and critical point theory, we guarantee the existence of infinitely many classical solutions for a two-point boundary value problem with fourth-order Sturm-Liouville equation; Some recent results are improved and by presenting one example, we ensure the applicability of our results.

Positive Solutions for Second-Order Singular Semipositone Boundary Value Problems

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,...

Multiple Positive Solutions for Singular Semipositone Periodic Boundary Value Problems with Derivative Dependence

Positive Symmetric Solutions of Singular Semipositone Boundary Value Problems

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...