 necessary aspect for sparring and self defense. Knowing how to take someone out won't do you much good if you pass out from lack of stamina.
Putting all 3 of these elements together gives us an expectational sport. It helps enhance your mind, body, and spirit by elevating your lifestyle. World Cup Karate and Fitness is more than just an activity for you or your child.  We help those who come through our door not only improve their lives for a short time, but to consistently boost their mindset and give them tools to live their best life ALWAYS!Hot Springs Police investigated what appeared to be a single vehicle crash on Airport Road last weekend.
A red Dodge Challenger driven by someone hopped the curb and slammed head-on into a concrete highway support beam underneath the Bypass. The vehicle became disabled and a female at the scene was arrested a short time after HSPD arrived on the scene. It is unknown to me why the female was arrested.
It is also unknown to me whether anyone was injured in connection to this crash. LifeNet Medics were not on scene before I departed. I left this scene early due to the triple shooting that took place in Fountain Lake at the same time. CLICK HERE for that story.
Traffic flow was interrupted for at least 45 minutes.Seriously, this was a huge win for me! I've been at #4 for Lions Mane kits for some time, and I stopped thinking about it for the last couple of weeks. Sure enough, there I was! If you couldn't tell in the video, I AM EXCITED! This means I am positioned to expand my operation to HIRE EMPLOYEES, GET THIS THING OUT OF MY HOME and start a proper business, or expand into other businesses to help run a tight ship! 

For now, the July 7lb Lions Mane kit pre-order is already nearing completion!! If you want to be one of the last ones for the July 15th delivery head over to [https://myctyson.com/shop/colonized-mushroom-substrates/7lb-lions-mane-substrate/](https://myctyson.com/shop/colonized-mushroom-substrates/7lb-lions-mane-substrate/) (or Google Lions Mane kits and shop around to see why my kits are the BEST value, you won't find 7lb kits anywhere else for the same pricing, especially for the 10 packs (EAST COAST HIT ME UP!)) and thanks for checking me out! 

PS Link to the $1 pre-pours here, just got my 21st ⭐⭐⭐⭐⭐ review on [https://myctyson.com/shop/mushroom-growing-supplies/pre-poured-agar-dishes-slants/](https://myctyson.com/shop/mushroom-growing-supplies/pre-poured-agar-dishes-slants/) and reduced my slant shipping pricing!Elliptic semi-linear systems on R\sp N

In this work we consider a system of k non-linear elliptic equations where the non-linear term is the sum of a quadratic form and a sub-critic term. We show that under suitable assumptions, e.g. when the non-linear term has a zero with non-zero coordinates, we can find a infinitely many solution of the eigenvalue problem with radial symmetry. Such problem arises when we search multiple standing-waves for a non-linear wave system.

We wish to find a k-tuple of standing waves, solution for the system, that is ψ ∈ C 2 (R, H 1 (R N, R k )) such that (2) ψ j (t, x) = u j (x)e −iωj t, u j (x) = 0, ω j ∈ R, 1 ≤ j ≤ k.
If V (z 1,..., z k ) = F (|z 1 |,..., |z k |), where F is a real-valued function on R k, the wave system becomes (3) − ∆u j + D j F (u 1,..., u k ) = ω 2 j u j, 1 ≤ j ≤ k. This work is an attempt to show the existence of standing-waves for a wide class of non-linearities which allow us to use a variational approach. For systems of Schroëdinger equations, we know of an existing work of B. Sirakov for coupled systems, [13]. For waves equations we know that, by means of numerical results, Y. Brihaye and B. Hartmann in [6] showed the existence of standing-waves. Following the notations used therein In this work, we provide a theorem of existence for arbitrary choices of k and N ≥ 3, where F is non-negative and can be written as the sum of a quadratic form on R k with eigenvalues m 1,..., m k and a non-linear term R satisfying the sub-critical growth condition |∇R(u)| ≤ c p−1 |u| p−1 + c q−1 |u| q−1, R(0) = 0 where 2 < p ≤ q < 2 *. Our aim is to obtain a solution (u i, ω i ) such that u i = 0, for certain values of ω i. The functional E and a constraint, M C (where C ∈ R k ) are defined as follows A common approach to this problem is to consider the more natural functional constrained to the Nehari manifold J ′ (u), u = 0, check for instance [8,13,16]. The advantage of considering the former functional follows from the fact that stationary points have positive eigenvalues. This approach was also followed in [2,4]. In Proposition 1, we prove that E : H 1 (R N ) → R is continuous and differentiable everywhere. This is known when R N is replaced by a bounded domain Ω, refer [11]. For unbounded domains, an adaption of the techniques used in [1] provides us with such result. We require the existence of (v, ω) ∈ R k × R k such that Such condition is fulfilled if, for instance, there exists v ∈ R k such that v i = 0 ∀i and F (v) = 0. This condition is referred in the text as H3). The main result is Theorem 1, where we prove that for arbitrarily large values of |C| there exists a radial solution of the elliptic system. We show that a minimizer of E over M r C, the functions on the constraints with radial symmetry, exists and, by the principle of symmetric criticality of Palais (refer [12]) we conclude that there exists a critical point on M C as well. The proof is made in two steps. In Lemma 2, we show that, for arbitrarily large values of |C|, In Proposition 4 we show that a Palais-Smale sequence (u n, ω n ) for has an H 1 -converging subsequence. The next goal is to prove the existence of solitons, that is, standing-waves which are stable with respect the dynamic corresponding to the initial-value problem of the wave equations. Check, for instance, [2], pag. 7, for a definition of soliton. The non-linear term we have in mind, when k = 2, is where T (u) = T (|u|) is a non-negative function. In the scalar case some results of general extent are due to W. Strauss in [14] and V. Benci, J. Bellazzini et al. in [3]. I would like to thank professor Vieri Benci and professor Jaeyoung Byeon for their helpful suggestions, as well as professors Pietro Majer, Claudio Bonanno and Jacopo Bellazzini.

Basic assumptions on the non-linear term
Given integers k, N ≥ 1, we denote by H 1 (R N, R k ) the set of functions u : R N → R k such that each component u i is in H 1 (R N ) and, by H 1 r (R N, R k ), those whose components are in H 1 (R N ) and radially symmetric. Hereafter, we will omit the domain and co-domain spaces from the notation when there is not ambiguity. We have the following inclusions where 2 * = 2N/(N − 2). For the proofs, check [5] and [14] respectively. Now, let F be a C 1, real-valued function on R k. We prove that there exists a weak solution u ∈ H 1 of the elliptic system H1) F is non-negative and there are m 1,..., m k positive, such that F can be written as where R is smooth and R(0) = 0; H2) there are constants c p−1, c q−1 ≥ 0 such that We will see how condition H3) ensures the existence of solutions of (3) with ω i < m i.
This definition can be extended to arbitrary functions spaces. The case of (L p (Ω), L r (Ω)) has been studied in [1] when Ω is a bounded domain and f is a Caratheodory function on Ω × R (that is, f (·, u) is measurable and f (x, ·) is continuous), and |f (x, u)| ≤ α + β|u| p/r.
Still