Critical Point Theory on Partially Ordered Hilbert Spaces

By Thomas Bartsch. 2001

143 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/a28981a25d872d7adf68e167f16cf7285f7756f7

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On the Existence and the Profile of Nodal solutions of Elliptic Equations Involving Critical Growth (2006, background): “The subcritical case is a particular case of problems treated in [8,10] where the authors studied the existence of sign changing solutions and their properties for a larger class of nonlinearities with subcritical growth.”
Nodal Solutions of a p‐Laplacian Equation (2005, background): “The proof which we present in this paper is di<erent from the one in [5] and more elementary in the sense that it does not use cohomological methods.”
Resonant nonlinear Neumann problems with indefinite weight (2012, unknown): “(6.41) But from Bartsch [4] and Liu-Wu [31] we know that Ck(φ λ +|C1n ($̄), u0) = Ck(φ λ +, u0) for all k ≥ 0 (6.42) and Ck(φ|C1n ($̄), u0) = Ck(φ, u0) for all k ≥ 0.”
Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem (2007, background): “Later, multiple sign changing solutions and their nodal properties were studied in [7,9].”
On a superlinear elliptic p-Laplacian equation (2004, result): “In particular, we generalize the above mentioned results from [1, 2, 4, 6, 8, 16, 17, 21] on the”
Schrödinger equations with concave and convex nonlinearities (2005, background): “The main idea in [ 3 , 17, 27, 28, 29] is to make use of the cones of positive functions and negative functions in C 1 0 (Ω).”
Sign Changing Solutions of Superlinear Schrödinger Equations (2003, methodology): “The results from [2] for Dirichlet problems on bounded domains suggest that (1.”
Finite time blow-up and global solutions for semilinear parabolic equations with initial data at high energy level (2005, background): “It is also known [3, 6], that (3) admits infinitely many nodal (sign-changing) solutions of arbitrarily high energy.”
A note on additional properties of sign changing solutions to superlinear elliptic equations (2003, methodology): “The Morse index of sign changing solutions with least energy We assume that (f1)–(f4) are in force throughout this section.”
Multiple solutions with precise sign for nonlinear parametric Robin problems (2014, unknown): “[4] T. Bartsch, Critical point theory on partially ordered Hilbert spaces, J. Funct.”