Existence of nontrivial solution for a nonlocal problem with subcritical nonlinearity

Existence of Nontrivial Solution for a Nonlocal Elliptic Equation with Nonlinear Boundary Condition

Existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem

In this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form $D_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0

existence and uniqueness of positive and nondecreasing solution for nonlocal fractional boundary value problem

in this article, we verify existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem of fractional differential equation in the form d_{0^{+}}^{alpha}x(t)+f(t,x(t))=0, 0x(0)= x'(0)=0, x'(1)=beta x(xi), where $d_{0^{+}}^{alpha}$ denotes the standard riemann-liouville fractional derivative, 0an illustrative example is also presented.

Existence of Nontrivial Solutions to Polyharmonic Equations with Subcritical and Critical Exponential Growth

The main purpose of this paper is to establish the existence of nontrivial solutions to semilinear polyharmonic equations with exponential growth at the subcritical or critical level. This growth condition is motivated by the Adams inequality [1] of Moser-Trudinger type. More precisely, we consider the semilinear elliptic equation (−∆) u = f(x, u), subject to the Dirichlet boundary condition u ...

Existence of Nontrivial Solutions for Singular Quasilinear Equations with Sign Changing Nonlinearity

By an application of Bonanno’s three critical point theorem, we establish the existence of a nontrivial solution to the problem −∆pu = μ g(x)|u|p−2u |x|p + λa(x)f(u) in Ω, u = 0 on ∂Ω, under some restrictions on g, a and f for certain positive values of μ and λ.