Existence and Asymptotic Profile of Nodal Solutions to Supercritical Problems

Existence of Nodal Solutions of Multi-point Boundary Value Problems

We study the nonlinear boundary value problem consisting of the equation y+w(t)f(y) = 0 on [a, b] and a multi-point boundary condition. By relating it to the eigenvalues of a linear Sturm-Liouville problem with a twopoint separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions of this problem. We also discuss the changes of the existence of different...

Existence of Global Solutions to Supercritical Semilinear Wave Equations

In this work we study the existence of global solution to the semilinear wave equation (∂

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.

Analysis of Blow-up Locus and Existence of Weak Solutions for Nonlinear Supercritical Problems

We give a qualitative analysis of sequences of stationary solutions to the supercritical problem −∆u = |u|p−1u in Ω, p > n + 2 n− 2 . A consequence of the analysis is the existence of positive singular weak solutions on a convex domain when p ∈ ( n−2 , n+1 n−3 ), with only isolated singularities.

EXISTENCE AND ASYMPTOTIC ANALYSIS OF SOLUTIONS OF SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS by