Solution curves of -th order boundary-value problems.
Solutions for -point BVP with sign changing nonlinearity.
Solutions to second order non-homogeneous multi-point bvps using a fixed-point theorem.
Solvability for second-order m-point boundary value problems at resonance on the half-line.
Solvability for two classes of higher-order multi-point boundary value problems at resonance.
Some remarks on three-point and four-point bvp's for second-order nonlinear differential equations.
Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions
Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials.
Strong singularities in mixed boundary value problems
We study singular boundary value problems with mixed boundary conditions of the form where We assume that satisfies the Carathéodory conditions on
Successive iteration and positive solutions for nonlinear -point boundary value problems on time scales.
Symmetric positive solutions for nonlinear singular fourth-order eigenvalue problems with nonlocal boundary condition.
Systems of singular BVPs - existence of solutions and their properties
We discuss the existence and properties of solutions for systems of singular second-order ODEs in both sublinear and superlinear cases. Our approach is based on the variational method enriched by some topological ideas. We also investigate the continuous dependence of solutions on functional parameters.
The existence and uniqueness of positive solutions for integral boundary value problems.
The existence of countably many positive solutions for nonlinear th-order three-point boundary value problems.
The existence of multiple positive solutions of -Laplacian boundary value problems
The existence of positive solution to a nonlinear fractional differential equation with integral boundary conditions.
The existence of positive solution to three-point singular boundary value problem of fractional differential equation.
The existence of positive solutions for nonlinear boundary system with -Laplacian operator based on sign-changing nonlinearities.
The existence of positive solutions for third-order -Laplacian -point boundary value problems with sign changing nonlinearity on time scales.
The shooting method and multiple solutions of two/multi-point BVPs of second-order ODE.
The shooting method and nonhomogeneous multipoint bvps of second-order ODE.