A Singular Semilinear Equation in L 1 (R)

1977 ◽  
Vol 225 ◽  
pp. 145 ◽  
Author(s):  
Michael G. Crandall ◽  
Lawrence C. Evans
Keyword(s):  
Semilinear Equation ◽  
Singular Semilinear Equation

scholarly journals Multiplicity results for sign changing bound state solutions of a semilinear equation

2015 ◽  
Vol 259 (12) ◽  
pp. 7108-7134 ◽  
Author(s):  
Carmen Cortázar ◽  
Marta García-Huidobro ◽  
Pilar Herreros
Keyword(s):  
Bound State ◽  
Multiplicity Results ◽  
Semilinear Equation

Existence of global solutions of a nonautonomous semilinear equation with varying reaction

2021 ◽  
pp. 1-13
Author(s):  
Ekaterina Todorova Kolkovska ◽  
José Alfredo López Mimbela ◽  
José Hermenegildo Ramírez González
Keyword(s):  
Global Solutions ◽  
Semilinear Equation

On a semilinear equation in ℝ2 involving bounded measures

1983 ◽  
Vol 95 (3-4) ◽  
pp. 181-202 ◽  
Author(s):  
Juan L. Vazquez
Keyword(s):  
Real Function ◽  
Radon Measure ◽  
Existence Of Solutions ◽  
Critical Value ◽  
Existence Of A Solution ◽  
One Dimensional ◽  
Semilinear Equation ◽  
The One

SynopsisWe study the semilinear equation –Δu + β(u) = f in ℝ2, where β is a continuous increasing real function with β(0) = 0 and f is a bounded Radon measure. We show the existence of a solution, which is unique in the appropriate class, provided that each of the point masses contained in f does not exceed some critical value denned in terms of the growth of (β at ∞ This condition is shown to be necessary for the existence of solutions, even locally. The one-dimensional situation is also discussed.

Existence of a bound state solution for quasilinear Schrödinger equations

2017 ◽  
Vol 8 (1) ◽  
pp. 323-338 ◽  
Author(s):  
Yan-Fang Xue ◽  
Chun-Lei Tang
Keyword(s):  
Nonlinear Term ◽  
Quasilinear Equation ◽  
Bound State ◽  
State Solution ◽  
Schrodinger Equations ◽  
Linking Theorem ◽  
Schrödinger Equations ◽  
Bound State Solution ◽  
Asymptotically Linear ◽  
Semilinear Equation

Abstract In this article, we establish the existence of bound state solutions for a class of quasilinear Schrödinger equations whose nonlinear term is asymptotically linear in {\mathbb{R}^{N}} . After changing the variables, the quasilinear equation becomes a semilinear equation, whose respective associated functional is well defined in {H^{1}(\mathbb{R}^{N})} . The proofs are based on the Pohozaev manifold and a linking theorem.

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