Nonlinear singular $ p $ -Laplacian boundary value problems in the frame of conformable derivative

Solutions of Nonlinear Singular Boundary Value Problems

We study the existence of solutions to a class of problems u + f(t, u) = 0, u(0) = u(1) = 0, where f(t, ·) is allowed to be singular at t = 0, t = 1.

Existence and Uniqueness of Solutions for Boundary Value Problems to the Singular One-Dimension p-Laplacian

Functional fractional boundary value problems with singular ϕ-Laplacian

This paper discusses the existence of solutions of the fractional differential equations D(φ(Du)) = Fu, D(φ(Du)) = f(t, u, Du) satisfying the boundary conditions u(0) = A(u), u(T ) = B(u). Here μ, α ∈ (0, 1], ν ∈ (0, α], D is the Caputo fractional derivative, φ ∈ C(−a, a) (a > 0), F is a continuous operator, A,B are bounded and continuous functionals and f ∈ C([0, T ] × R). The existence result...

Existence of Positive Solutions for Singular P-laplacian Sturm-liouville Boundary Value Problems

We prove the existence of positive solutions of the Sturm-Liouville boundary value problem −(r(t)φ(u′))′ = λg(t)f(t, u), t ∈ (0, 1), au(0)− bφ−1(r(0))u′(0) = 0, cu(1) + dφ−1(r(1))u′(1) = 0, where φ(u′) = |u′|p−2u′, p > 1, f : (0, 1) × (0,∞) → R satisfies a p-sublinear condition and is allowed to be singular at u = 0 with semipositone structure. Our results extend previously known results in the...

Positive Solutions of Three-point Boundary-value Problems for P-laplacian Singular Differential Equations

In this paper we prove the existence of positive solutions for the three-point singular boundary-value problem −[φp(u)] = q(t)f(t, u(t)), 0 < t < 1 subject to u(0)− g(u′(0)) = 0, u(1)− βu(η) = 0 or to u(0)− αu(η) = 0, u(1) + g(u′(1)) = 0, where φp is the p-Laplacian operator, 0 < η < 1; 0 < α, β < 1 are fixed points and g is a monotone continuous function defined on the real line R with g(0) = ...