Normalized Solutions to Strongly Indefinite Semilinear Equations

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Weakly and strongly singular solutions of semilinear fractional elliptic equations

If p ∈ (0, N N−2α ), α ∈ (0, 1), k > 0 and Ω ⊂ R is a bounded C domain containing 0 and δ0 is the Dirac measure at 0, we prove that the weak solution of (E)k (−∆) u + u = kδ0 in Ω which vanishes in Ω is a weak singular solution of (E)∞ (−∆) u + u = 0 in Ω \ {0} with the same outer data. Furthermore, we study the limit of weak solutions of (E)k when k → ∞. For p ∈ (0, 1+ 2α N ], the limit is inf...

Multi-bump Solutions for a Strongly Indefinite Semilinear Schrödinger Equation Without Symmetry or convexity Assumptions

In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + V (x)u = f(x, u), u ∈ H1(RN). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x, t) satisfies some superlinear growth conditions and need not be odd or increasing strictly in t. Using a new variational reduction method and a generaliz...

The Nehari Manifold for a Class of Indefinite Weight Semilinear Elliptic Equations

Existence of a Nontrivial Solution to a Strongly Indefinite Semilinear Equation

Under general hypotheses, we prove the existence of a nontrivial solution for the equation Lu = N(u), where u belongs to a Hilbert space H , L is an invertible continuous selfadjoint operator, and N is superlinear. We are particularly interested in the case where L is strongly indefinite and N is not compact. We apply the result to the Choquard-Pekar equation -Au(x)+p(x)u(x) = u(x) f U <'y\ dy,...