Abstract. We consider a class of singular systems of Lane-Emden type ⎪ ⎨ ∆u + λu p1vq1 = 0, x ∈ D, ∆v + λup2vq2 = 0, x ∈ D, u = v = 0, x ∈ ∂D, with p1 ≤ 0, p2> 0, q1> 0, q2...
Nonlinear Differential Equations, (2008)
ftp ejde.math.swt.edu or ejde.math.unt.edu (login: ftp) Instability and exact multiplicity of solutions of semilinear equations ∗
Philip Korman, Alan C. Lazer, Yi Li
We extend some earlier results on existence of homoclinic solutions for a class of Hamiltonian systems. We also study heteroclinic solutions. We use variational approach. 1
Philip Korman, Yi Li, Tiancheng Ouyang
For a class of Dirichlet problems in two dimensions, generalizing the model case ∆u + λu(u − b)(c − u) =0 in |x | <R,u=0 on |x | = R, ∗ Supported in part by the National Science...
For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results....
For a class of two-point boundary value problems we prove exactness of S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like e...
A global approach to ground state solutions (2008)
We study radial solutions of semilinear Laplace equations. We try to understand all solutions of the problem, regardless of the boundary behavior. It turns out that one can study uniqueness or...
On the Exactness of an S-Shaped Bifurcation Curve (2007)
For a class of two-point boundary value problems we prove exactness of S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities like e...
Philip Korman, Yi Li, K. Schmitt, D. Costa, ...
We use bifurcation theory to show the existence of infinitely many solutions at the first eigenvalue for a class of Dirichlet problems in one dimension. It has been observed that complexity of the...
For very general two-point boundary value problems we show that any positive solution satisfies a certain integral relation. As a consequence we obtain some new uniqueness and multiplicity results....
Philip Korman, Alan C. Lazer, Yi Li
We extend some earlier results on existence of homoclinic solutions for a class of Hamiltonian systems. We also study heteroclinic solutions. We use variational approach. 1
Philip Korman, Yi Li, Tiancheng Ouyang
We present exact multiplicity results for the boundary value problems of the type
Philip Korman, Yi Li, Tiancheng Ouyang
For a class of Dirichlet problems in two dimensions, generalizing the model case #u + #u(u b)(c u) = 0 in
Homoclinic orbits for a class of symmetric Hamiltonian systems (2007)
We study existence of homoclinic orbits for a class of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a...
On the direction of pitchfork bifurcation (2007)
Xiaojie Hou, Philip Korman, Yi Li
We present an algorithm for computing the direction of pitchfork bifurcation for two-point boundary value problems. The formula is rather involved, but its computational evaluation is quite feasible....
Similarity of solution branches for two-point semilinear problems (2003)
For semilinear autonomous two-point problems, we show that all Neumann branches and all Dirichlet branches with odd number of interior roots have the same shape. On the other hand, Dirichlet branches...
New Exact Multiplicity Results With an Application to a Population Model (2001)
We obtain some new exact multiplicity results for the Dirichlet boundary value problem u + f(u) = 0 for x 2 B n ; u = 0 for x 2 @B n ; on a unit ball B n in R n . We consider several classes of...
Infinitely many solutions at a resonance (2000)
We use bifurcation theory to show the existence of infinitely many solutions at the first eigenvalue for a class of Dirichlet problems in one dimension.
Instability and exact multiplicity of solutions of semilinear equations (2000)
For a class of two-point boundary-value problems we use bifurcation theory to show that a solution is unstable under a simple, geometric in nature, assumption on the non-linear term. As an...
On the exactness of an S-shaped bifurcation curve (1999)
Abstract. For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities...
On the exactness of an S-shaped bifurcation curve (1999)
Abstract. For a class of two-point boundary value problems we prove exactness of an S-shaped bifurcation curve. Our result applies to a problem from combustion theory, which involves nonlinearities...
A global solution curve for a class of semilinear equations (1998)
We use bifurcation theory to give a simple proof of existence and uniqueness of a positive solution for the problem $$ Delta u - lambda u+u^p = 0 quad mbox{for } |x| < 1, quad u = 0 quad mbox{on }...
An Exact Multiplicity Result For A Class Of Semilinear Equations (1997)
Philip Korman, Yi Li, Tiancheng Ouyang
For a class of Dirichlet problems in two dimensions, generalizing the model case \Deltau + u(u \Gamma b)(c \Gamma u) = 0 in jxj ! R; u = 0 on jxj = R; Supported in part by the National Science...
Exact multiplicity results for boundary value problems with nonlinearities generalising cubic (1996)
Homoclinic orbits for a class of symmetric Hamiltonian systems (1994)
of Hamiltonian systems that are symmetric with respect to independent variable (time). For the scalar case we prove existence and uniqueness of a positive homoclinic solution. For the system case we...
Computation of displacements for nonlinear elastic beam models using monotone iterations (1988)
We study displacement of a uniform elastic beam subject to various physically important boundary conditions. Using monotone methods, we discuss stability and instability of solutions. We present...
Computation of displacements for nonlinear elastic beam models using monotone iterations (1988)
We study displacement of a uniform elastic beam subject to various physically important boundary conditions. Using monotone methods, we discuss stability and instability of solutions. We present...
Existence of solutions for a nonlinear boundary value problem associated with water waves / (1981)
Typescript.
Thesis (Ed. D.)--University of Southern California, 1974.