# Positive solutions of ...u +u p =0 whose singular set is a manifold with boundary

## Related Articles

- The Nehari manifold for a semilinear elliptic equation involving a sublinear term. Brown, K. // Calculus of Variations & Partial Differential Equations;Apr2005, Vol. 22 Issue 4, p483
The Nehari manifold for the equationfortogether with Dirichlet boundary conditions is investigated in the case where. Exploiting the relationship between the Nehari manifold and fibrering maps (i.e., maps of the formwhereJis the Euler functional associated with the equation), we discuss how the...

- EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR KIRCHHOFF TYPE PROBLEM WITH CRITICAL EXPONENT. QI-LIN XIE; XING-PING WU; CHUN-LEI TANG // Communications on Pure & Applied Analysis;Nov2013, Vol. 12 Issue 6, p2773
In the present paper, the existence and multiplicity of solutions for Kirchhoff type problem involving critical exponent with Dirichlet boundary value conditions are obtained via the variational method.

- An Estimate of the First Eigenvalue in a Many-Point Boundary Value Problem. Knezevic-Miljanovic, J. // Differential Equations;Dec2003, Vol. 39 Issue 12, p1802
This article presents an estimate of the first eigenvalue in a many-point boundary value problem. It follows from the classical theory of linear spectral problems that the spectrum of problem is real, discrete, and positive. The eigenfunction corresponding to the minimum eigenvalue has n zeros...

- Variational problem for a gas journal bearing. Boldyrev, Yu.; Petukhov, E. // Fluid Dynamics;Mar2015, Vol. 50 Issue 2, p193
A variational problem for a gas journal bearing is considered in the one-dimensional formulation. The feature of the problem relates to the fact that an additional condition of gas exchange with the surrounding medium, namely, the Elrod-Burgdorfer condition, is used in the Reynolds equation. The...

- EXISTENCE OF SOLUTIONS FOR A SECOND ORDER PROBLEM ON THE HALF-LINE VIA EKELAND'S VARIATIONAL PRINCIPLE. BOUAFIA, D.; MOUSSAOUI, T.; O'REGAN, D. // Discussiones Mathematicae: Differential Inclusions, Control & Op;2016, Vol. 36 Issue 2, p131
In this paper we study the existence of nontrivial solutions for a nonlinear boundary value problem posed on the half-line. Our approach is based on Ekeland's variational principle.

- Spectral Analysis and Zeta Determinant on the Deformed Spheres. Spreafico, M.; Zerbini, S. // Communications in Mathematical Physics;Jul2007, Vol. 273 Issue 3, p677
We consider a class of singular Riemannian manifolds, the deformed spheres $${S^{N}_{k}}$$ , defined as the classical spheres with a one parameter family g[ k] of singular Riemannian structures, that reduces for k = 1 to the classical metric. After giving explicit formulas for the eigenvalues...

- Existence of complete conformal metrics of negative Ricci curvature on manifolds with boundary. Gursky, Matthew; Streets, Jeffrey; Warren, Micah // Calculus of Variations & Partial Differential Equations;May2011, Vol. 41 Issue 1/2, p21
We show that on a compact Riemannian manifold with boundary there exists $${u \in C^{\infty}(M)}$$ such that, u â‰¡ 0 and u solves the Ïƒ-Ricci problem. In the case k = n the metric has negative Ricci curvature. Furthermore, we show the existence of a complete conformally related metric on...

- Some new PDE methods for weak KAM theory. Evans, Lawrence C. // Calculus of Variations & Partial Differential Equations;Jun2003, Vol. 17 Issue 2, p159
We discuss a new approximate variational principle for weak KAM theory. The advantage of this approach is that we build both a minimizing measure and a solution of the generalized eikonal equation at the same time. Furthermore the approximations are smooth, and so we can derive some interesting...

- THE HARDY INEQUALITY WITH ONE NEGATIVE PARAMETER. Kufner, A.; Kuliev, K.; Kulieva, G. // Banach Journal of Mathematical Analysis;2008, Vol. 2 Issue 2, p76
In this paper, necessary and sufficient conditions for the validity of the Hardy inequality for the case q < 0, p > 0 and for the case q > 0, p < 0 are derived.