5 papers · 1 filter
Bounded solutions for a class of Hamiltonian systems
Philip Korman, Guanying Peng
We obtain bounded for all solutions of ordinary differential equations as limits of the solutions of the corresponding Dirichlet problems on , with $L \rightarrow \inft…
Explicit solutions and multiplicity results for some equations with the -Laplacian
Philip Korman
We derive explicit ground state solutions for several equations with the -Laplacian in , including (here , with ) \[ φ\left(u'(r)\right)' +\frac{n-1}{…
Nonlinear elliptic equations and systems with linear part at resonance
Philip Korman
The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues.…
Families of solution curves for some non-autonomous problems
Philip Korman
The paper studies families of positive solution curves for non-autonomous two-point problems \[ u"+λf(u)-μg(x)=0, \;\; -1<x<1, \;\; u(-1)=u(1)=0 \] depending on two positive parame…
Infinitely many solutions for three classes of self-similar equations, with the -Laplace operator
Philip Korman
We study the global solution curves, and prove the existence of infinitely many positive solutions for three classes of self-similar equations, with -Laplace operator. In case $…