I tried a lot of things but it seems that my "searchservice" in my jersey ressource instantiate itself randomly. SearchService in SearchResource is almost always null.
As you can see I added spring-jersey dependency.
Here is my code : SearchResource (jersey, try to instantiante searchService)
@Path("search")
@Component
public class SearchResource {
    private static final Logger LOGGER = Logger.getLogger(SearchResource.class);
    @Context
    private UriInfo context;
    @Autowired
    private SearchService searchService;
    /**
     * Creates a new instance of SearchResource
     */
    public SearchResource() {
    }
    /**
     * Retrieves representation of an instance of com.gehc.mpse.backend.ws.SearchResource
     * @param search
     * @param <error>
     * @param authors
     * @return an instance of java.lang.String
     */
    @GET
    @Produces(MediaType.APPLICATION_JSON)
    public Response search(@QueryParam("query") String search, @QueryParam("authors") List<String> authors) {
        System.out.println("searchservice :" + searchService);
        Response res = searchService.searchQuery(search);
        return res;
    }
    public SearchService getSearchService() {
        return searchService;
    }
    public void setSearchService(SearchService searchService) {
        this.searchService = searchService;
    }
My class searchService :
@Component
public class SearchService {
    private static final Logger LOGGER = Logger.getLogger(SearchService.class);
    @Autowired
    private IPublicationRepository repository;
    @Autowired
    private Neo4jTemplate template;
    private static final Integer PAGE_SIZE = 20;
    public SearchService() {
        LOGGER.debug("search service initialzed " + this);
    }
    public Response searchQuery(String query) {
        PageRequest request
                = new PageRequest(1, PAGE_SIZE);
        LOGGER.debug("repo : " + repository);
        Page<Publication> res = repository.findPublicationByTitle(query, request);
        //repository.query(query, null);
        return Response.ok().entity(res.getContent()).build();
    }
    public IPublicationRepository getRepository() {
        return repository;
    }
    public void setRepository(IPublicationRepository repository) {
        this.repository = repository;
    }
    public Neo4jTemplate getTemplate() {
        return template;
    }
    public void setTemplate(Neo4jTemplate template) {
        this.template = template;
    }
}
My pom.xml
<dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-core</artifactId>
        <version>${spring.version}</version>
        <exclusions>
            <exclusion>
                <groupId>commons-logging</groupId>
                <artifactId>commons-logging</artifactId>
            </exclusion>
        </exclusions>
    </dependency>
    <dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-context</artifactId>
        <version>${spring.version}</version>
    </dependency>
    <dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-context-support</artifactId>
        <version>${spring.version}</version>
    </dependency>
    <dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-web</artifactId>
        <version>${spring.version}</version>
        <scope>compile</scope>
    </dependency>
    <dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-beans</artifactId>
        <version>${spring.version}</version>
    </dependency>
    <dependency>
        <groupId>org.springframework</groupId>
        <artifactId>spring-tx</artifactId>
        <version>${spring.version}</version>
    </dependency>
    <dependency>
        <groupId>org.springframework.data</groupId>
        <artifactId>spring-data-neo4j</artifactId>
        <version>3.2.0.RELEASE</version>
        <exclusions>
            <exclusion>
                <groupId>org.neo4j</groupId>
                <artifactId>neo4j</artifactId>
            </exclusion>
            <exclusion>
                <groupId>org.neo4j</groupId>
                <artifactId>neo4j-cypher</artifactId>
            </exclusion>
            <exclusion>
                <groupId>org.neo4j</groupId>
                <artifactId>neo4j-kernel</artifactId>
            </exclusion>
        </exclusions>
    </dependency>
    <!-- Spring [End] -->
    <!--neo4j -->
    <dependency>
        <groupId>org.neo4j</groupId>
        <artifactId>neo4j</artifactId>
        <version>2.1.5</version>
    </dependency>
    <dependency>
        <groupId>org.neo4j.app</groupId>
        <artifactId>neo4j-server</artifactId>
        <version>2.1.5</version>
    </dependency>
    <!-- end neo4j -->
    <dependency>
        <groupId>org.glassfish.metro</groupId>
        <artifactId>webservices-rt</artifactId>
        <version>2.3</version>
        <scope>provided</scope>
    </dependency>
    <dependency>
        <groupId>javax</groupId>
        <artifactId>javaee-web-api</artifactId>
        <version>7.0</version>
        <scope>provided</scope>
    </dependency>
    <dependency>
        <groupId>org.slf4j</groupId>
        <artifactId>slf4j-api</artifactId>
        <version>1.7.7</version>
    </dependency>
    <dependency>
        <groupId>org.slf4j</groupId>
        <artifactId>slf4j-log4j12</artifactId>
        <version>1.7.7</version>
    </dependency>
    <dependency>
        <groupId>org.apache.axis2</groupId>
        <artifactId>axis2</artifactId>
        <version>1.6.2</version>
    </dependency>
    <dependency>
        <groupId>org.apache.axis2</groupId>
        <artifactId>axis2-java2wsdl</artifactId>
        <version>1.6.2</version>
    </dependency>
    <dependency>
        <groupId>org.apache.ws.commons.axiom</groupId>
        <artifactId>axiom-api</artifactId>
        <version>1.2.14</version>
    </dependency>
    <dependency>
        <groupId>org.apache.ws.commons.axiom</groupId>
        <artifactId>axiom-impl</artifactId>
        <version>1.2.14</version>
    </dependency>
    <dependency>
        <groupId>org.reflections</groupId>
        <artifactId>reflections</artifactId>
        <version>0.9.9-RC1</version>
    </dependency>
    <dependency>
        <groupId>org.glassfish.jersey.ext</groupId>
        <artifactId>jersey-spring3</artifactId>
        <version>2.13</version>
        <exclusions>
            <exclusion>
                <groupId>org.springframework</groupId>
                <artifactId>spring</artifactId>
            </exclusion>
            <exclusion>
                <groupId>org.springframework</groupId>
                <artifactId>spring-core</artifactId>
            </exclusion>            
            <exclusion>
                <groupId>org.springframework</groupId>
                <artifactId>spring-web</artifactId>
            </exclusion>
            <exclusion>
                <groupId>org.springframework</groupId>
                <artifactId>spring-beans</artifactId>
            </exclusion>
            <exclusion>
                <groupId>org.glassfish.jersey.core</groupId>
                <artifactId>jersey-server</artifactId>
            </exclusion>
            <exclusion>
                <groupId>org.glassfish.jersey.containers</groupId>
                <artifactId>jersey-container-servlet-core</artifactId>
            </exclusion>
            <exclusion>
                <groupId>org.glassfish.hk2</groupId>
                <artifactId>hk2</artifactId>
            </exclusion>
        </exclusions>
    </dependency>
    <dependency>
        <groupId>org.glassfish.jersey.media</groupId>
        <artifactId>jersey-media-json-jackson</artifactId>
        <version>2.13</version>
        <scope>provided</scope>
    </dependency>
</dependencies>
My web.xml :
<web-app version="3.0" xmlns="http://java.sun.com/xml/ns/javaee"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="http://java.sun.com/xml/ns/javaee http://java.sun.com/xml/ns/javaee/web-app_3_0.xsd">
    <display-name>PMSE</display-name>
    <listener>
        <listener-class>
            org.springframework.web.context.ContextLoaderListener
        </listener-class>
    </listener>
    <listener>
        <listener-class>
            org.springframework.web.context.request.RequestContextListener
        </listener-class>
    </listener>
    <context-param>
        <param-name>contextConfigLocation</param-name>
        <param-value>classpath*:spring/context.xml</param-value>
    </context-param>
</web-app>